Korn type inequalities in orlicz spaces andrea cianchi universit a di firenze, italy ban, july 2016 a. Demonstrate that the moduli space is alh by computing its asymptotic. In the first of them, various ways to construct and compactify moduli spaces are presented. Such spaces frequently arise as solutions to classification problems. This was known for n 0 in the same range, by the work of igusa, shepherdbarron and katsylo. For example, the moduli space of semistable sheaves in the sense of gieseker with xed hilbert. Clay mathematics institute workshop moduli spaces of vector bundles, with a view towards coherent sheaves october 611, 2006 cambridge, massachusetts clay mathematics proceedings volume 14 grassmannians, moduli spaces and vector bundles clay mathematics institute, cambridge, ma p. You should be reasonably familiar with these spaces and other nite dimensional vector spaces. Orlicz sequence spaces generalize the spaces, and as such play an important role in functional analysis definition. Thus the space of all such conformal structures, called the moduli space, is the interval 1.
The vector spaces kn consisting of ordered ntuples of elements of k. The slope stability of the logarithmic cotangent bundle of the dm moduli spaces, chern number inequality and other properties will follow. We construct a kahler metric on the moduli spaces of compact complex manifolds with c 1, and moduli spaces edited by org. Page 1 geometricquantizationfor themodulispaceofvector bundleswithparabolicstructure georgios d. Moduli spaces can be thought of as giving a universal space of parameters for the problem.
Nef divisors for moduli spaces of complexes with compact support 3 returning to the proof of theorem1. It is proven that the composition of the yoneda coupling with the semiregularity map is a closed 2formon moduli spaces of sheaves. In mathematics, an orlicz sequence space is any of certain class of linear spaces of scalarvalued sequences, endowed with a special norm, specified below, under which it forms a banach space. Here different solutions are identified if they are isomorphic that is, geometrically the same.
If you want k v so you have to trim them and accept that no key or value of yours contains spaces at start and end of string. A way of answering the first and the second questions is analyzing the origin of the structure of the complexes. Penrose transform on dmodules, moduli spaces and field. We consider here compacti cations of the space of maps from curves to grassmannians. N 2 gauge theories, instanton moduli spaces and geometric representation theory 1 richard j. An orlicz extension of difference modular sequence. The theorys principal application is to the construction of various moduli spaces. The proof uses the ne moduli space of stable npointed rational curves and the coarse moduli space of kontsevich stable npointed maps, which are used to parametrise the rational plane curves that feature in the formula. Moreover, the study of moduli spaces has benefited tremendously in recent years from interactions with physics in. Several topics in these notes will not be covered and some may be discussed only brie y in the. This later space comes with a natural orbicellular structure given by ribbon graphs.
Tropical orbit spaces and moduli spaces of tropical curves. Such moduli spaces have two di erent branches, named higgs branch and coulomb branch, joined at the origin, which in turn corresponds to a. Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. Its cohomology ring has a elegant structure, and mumford suggested studying the moduli space of curves in the same way. Curve complexes and the dmcompactification of moduli spaces. Pdf an orlicz extension of difference modular sequence.
Deligne products of line bundles over moduli spaces of curves. The geometry of moduli spaces of sheaves daniel huybrechts download here now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive. Summary by m gm,n we denote the moduli space of conformal structures on an oriented compact cobordism s gm,n of genus g. That is, the points of a moduli space correspond to solutions of geometric problems. Hyperpolygon spaces and moduli spaces of parabolic higgs bundles. In mathematics, in particular algebraic geometry, a moduli space is a geometric space whose points represent algebrogeometric objects of some fixed kind, or isomorphism classes of such objects. How to include spaces between equal sign when working with. Shingtung yau geometry of the moduli space of curves. Conjugate functions, conjugate series, singular integrals 46e30. Some generalized difference sequence spaces defined by a. What is a good introductory text for moduli theory. Newstead gave a series of lectures in 1975 at the tata institute of fundamental research, mumbai, on git and its application to the moduli of vector bundles on curves. Git constructions of moduli spaces of stable curves and maps 319 result from using a.
The irreducibility of the space of curves of given genus pdf. Di culties in the construction of moduli spaces in general, cannot construct a moduli space of a class of objects if each object has lots of automorphisms. Compactified moduli spaces of rational curves in projective homogeneous varieties chung, kiryong, hong, jaehyun, and kiem, younghoon, journal of the mathematical society of japan, 2012. New moduli spaces of pointed curves and pencils of flat connections. Git constructions of moduli spaces of stable curves and maps. Moduli spaces of covers constitute an appropriate tool for certain arithmetic problems involving algebraic curves and rational functions. We also describe singularities and some other features of it. For example, if we try to construct a moduli space of spheres pc2, we run into trouble because they can be \spun around. Some generalized difference sequence spaces defined by a sequence of moduli in normed spaces abdullah alotaibi, 1 kuldip raj, 2 and s. Moduli spaces of stable vector bundles on enriques. Section 1 is an informal introduction to moduli spaces of smooth and stable curves.
Anyway, here i would be interested to know of other examples more in the vein of the mo question linked above. Part of the lecture notes in mathematics book series lnm, volume 1034 log in to check access. Introduction let x be an artin stack always assumed to have quasicompact and separated diagonal over specz. When g 3, it is the moduli space of smooth projective curves c, together with nordered distinct points and a symplectic basis of h1c. Many moduli spaces in algebraic geometry are constructed as git quotients yg where y is a parameter space for some collection of algebrogeometric objects and the gorbits correspond to equivalence classes of these objects. Inequalities in approximation bernstein, jackson, nikol s kiitype inequalities secondary. On arithmetic curves in the moduli spaces of curves. A moduli space is usually the set of isomorphism classes of objects of a given type.
Nevertheless, something is known about the type of singularities they can attain. The aim of the conference is to gather experts in various e. Log fano varieties, mori dream spaces and moduli spaces of. In section 1 we discuss the general problem of constructing.
The perturbed ricci metric that we introduced has bounded. Rate of convergence, degree of approximation 41a27. Notes on the construction of the moduli space of curves dan edidin the purpose of these notes is to discuss the problem of moduli for curves of genus g. Upr843t, pupt1856 moduli spaces of fivebranes on elliptic calabiyau threefolds ron donagi1,burta. We introduce the concepts of moduli spaces, of stable curves and of stable maps in our exposition, and sketch the. The institute is located at 17 gauss way, on the university of california, berkeley campus, close to grizzly peak, on the. We study deligne products for forgetful maps between moduli spaces of marked curves by offering a closed formula for tautological line bundles associated to marked points. Torsion subgroups of jacobians acting on moduli spaces of vector bundles frank nasser opalgtopgeo maphysto department of mathematics university of aarhus, denmark. The method of parametrizing moduli spaces by subsets of hilbert schemes, yields a natural compactification, since hilbert schemes are projective, but since all isomorphism classes of the original type were already present before compactifying, it is unclear what geometric objects the new points added correspond to. I added a few words outlining other work of harer on the stability of the cohomology of the moduli space of curves. What links here related changes upload file special pages permanent link. The properties of four elements in orliczmusielak spaces. Torelli groups and geometry of moduli spaces of curves. Logan also has a table of unirational moduli spaces, for 2 g 9 and g 11, and nat most equal to fg.
Thus our moduli space will be one of the equivalences of the conformal classes given in the. Other good introductions to moduli spaces include 10 and 20. Moduli spaces of fivebranes on elliptic calabiyau threefolds. Funtional analysis lecture notes for 18 mit mathematics. Firenze korn inequalities in orlicz spaces banff, july 2016 1 38. From this we induce a onetoone correspondence between these moduli spaces and calculate the dimension of the atwisted. Moduli spaces london mathematical society lecture note. An introduction to moduli spaces of curves and its. Moduli spaces of local systems and higher teichmuller theory. Submitted on 10 nov 2003 v1, last revised 29 apr 2006 this. Ovrut2and daniel waldram3 1department of mathematics, university of pennsylvania philadelphia, pa 191046395, usa 2department of physics, university of pennsylvania philadelphia, pa 191046396, usa. Concerning the geometry of moduli spaces of sheaves of higher rank, there.
T can be recovered from l teand the action of z2 by translations. Improved converse theorems and fractional moduli of smoothness in orlicz spaces article pdf available in the bulletin of the malaysian mathematical society series 2 361. But the main strategy is to replace polynomial divergence by the \exponential drift idea of benoistquint bq. Moduli stacks of semistable sheaves and representations of extquivers toda. Theproperty offourelements pfe,closely related totheisotonicity ofthemetric projection operator, has been recently introduced and proved in ordered hilbert spaces, lp spaces and orliczmusielak spaces see 5, 6, 12. The content ranges from the definition of a semistable sheaf and its basic properties over the construction of. Some of the ideas came from discussions with amir mohammadi. Perhaps the simplest way to see this is to note that, by standard topology, since xn g is contractible, each element of. In mathematics, in particular algebraic geometry, a moduli space is a geometric space whose. Pdf improved converse theorems and fractional moduli of. This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. We show that the image of the moduli space of stable bundles on an enriques surface by the pull back map is a lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering k3 surface. Given an ntuple of positive real numbers \alpha we consider the hyperpolygon space x\alpha, the hyperkahler quotient analogue to.
Here is wayback machine ink to the site and to the pdf file. This construction uses various types of cohomology classes on the moduli spaces, namely the double ramification cycles, other natural tautological classes like the hodge and psi classes, and cohomological field theories. Two riemann surfaces of the same topological type can, of course, be con formally inequivalent. To study many aspects of moduli theory in a simple setting motivates us to begin our exploration with the grassmannian. Page 1 geometricquantizationfor themodulispaceofvector. In the present work we investigate the approximation of the functions by zygmund means in the orlicz spaces l mt in the terms of the best approximation e n f m and modulus of smoothness. Invite leading researchers to give talks on recent results and the latest developments in the field. Pdf in this paper we construct some new difference modular sequence spaces defined by a sequence of orlicz functions over nnormed spaces. Introduce graduate students and young researchers to the latest research and open problems in the. Geometry, topology and dynamics of moduli spaces ims. Metric and analytic aspects of moduli spaces four week. Some problems on best approximation in orlicz spaces author. One cou ples the given git problem to a simpler one having the same symmetry group, and then studies the master space associated with the coupling as a c space. Karen vogtmann moduli spaces and their compacti cations 5 2.
We initiate a study of the geometric quantization of chernsimons gauge theory on riemann surfaces with punctures. If you want custome ini file, pm me and i will give you source code of my ini class, maybe 12 hours later hungpv jul 17 15 at 16. Moduli spaces of higgs bundles in mathematics and physics. Smoothness on bubble tree compactified instanton moduli spaces article in acta mathematica sinica 262. Ingeometryoneusuallywantstodefineinvariantsof thespaces,orgeometricobjects,underconsideration. Followup on collaborative work from previous ims programs. Clay mathematics proceedings volume 10 homogeneous. Szabo department of mathematics, heriotwatt university colin maclaurin building, riccarton, edinburgh eh14 4as, uk and maxwell institute for mathematical sciences, edinburgh, uk and the higgs centre for theoretical physics, edinburgh, uk. Torsion subgroups of jacobians acting on moduli spaces of. Mohiuddine 1 1 operator theory and applications research group, department of mathematics, faculty of science, king abdulaziz university, p. On the moduli and characteristic of monotonicity in orliczlorentz function spaces henryk hudzik faculty of mathematics and computer sciences adam mickiewicz university poznan, poland email. Metric and analytic aspects of moduli spaces four week program at the isaac newton institute, july 20 august 15, 2015 the goal of this program was to draw together experts working on moduli spaces arising in geometric analysis and mathematical physics, with an emphasis on new analytic and. Geometry and dynamics on moduli spaces clay mathematics. If one can show that a collection of interesting objects can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space.
The moduli space m g,m is a complex orbifold, as a quotient of t g,m by mapping class group mod g,m. Some notes containing a brief survey of the cohomology of the moduli space of curves and the harerzagier formula for the orbifold euler characteristic. On the moduli and characteristic of monotonicity in orlicz. The lecture notes section lists the lecture topics, along with the lecture notes files, covered in the course. The properties of four elements in orliczmusielak spaces bartosz micherda abstract. Im aware of the relation between hilbert schemes and also other kinds of moduli spaces of sheaves and instantons.
Addition is by components and the action of k is by multiplication on all components. The mathematical sciences research institute msri, founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the national science foundation, foundations, corporations, and more than 90 universities and institutions. Finite group actions on the moduli space of selfdual connections. Put simply, a stack is the quotient of a scheme by a group action. Two examples aregiven when this 2formis symplectic. Some problems on best approximation in orlicz spaces. In kon92 kontsevich introduces a way to compactify this space in order to prove wittens conjecture. We introduce the moduli space of genus, pointed curves, with enough information. Pdf finite group actions on the moduli space of selfdual. Aug 19, 2016 bring together experts who study the geometry, topology and dynamics of moduli spaces. Derived di erential geometry derived di erential geometry ddg is the study of derived smooth manifolds and derived smooth orbifolds, where derived is. The goal of this article is to motivate and describe how gromovwitten theory can and has provided tools to understand the moduli space of curves. Smoothness on bubble tree compactified instanton moduli spaces.
Moduli spaces in applied mathematics and condensed matter. We discuss interesting families of moduli spaces of charge 5 lumps using the symmetry property and riemannhurwitz formula. Moduli spaces are spaces of solutions of geometric classification problems. In chapter 4 we will focus on some particular and well understood examples of mori dream space arising as blowups of projective spaces in points, and we will discuss their relations with some moduli spaces of weighted rational curves.
Three contributions give an insight on particular aspects of moduli problems. In particular, we show that the deligne products for line bundles on the total spaces corresponding to forgotten marked points are positive integral multiples. Moduli spaces of higgs bundles in mathematics and physics yan soibelman kansas state university november 19, 20 yan soibelman kansas state university moduli spaces of higgs bundles in mathematics and physicsnovember 19, 20 1 33. Approximation of periodic functions by zygmund means in. The metric on the moduli spaces of vortices on compact riemann surfaces where the. Operads and moduli spaces thesis submitted for the degree of doctor of philosophy at the university of leicester christopher braun department of mathematics university of leicester arxiv. Given an f qlinear category such that the moduli space of its objects is a smooth artin.
The purpose of this conference is to bring together mathematicians working in the field of moduli spaces of geometric and algebraic structures which might be related to mathematical aspects of quantization. For elliptic curves they correspond respectively to the j and. Symplectic geometry on moduli spaces of stable pairs numdam. Bundles over moduli spaces and the quantisation of bps monopoles. In section 1 we consider the moduli space mr, d, l of stable pairs as constructed by. In this paper we studied some problems on best approximation in orlicz spaces, for which the approximating sets are haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result. Clay mathematics proceedings volume 14 grassmannians. New moduli spaces of pointed curves and pencils of. The geometry of moduli spaces of sheaves daniel huybrechts. Given an f qlinear category such that the moduli space of its objects is a smooth artin stack and some additional conditions we give formulas for an exponential sum over the set of abso. Moduli spaces of sheaves of rank 2 on a surface are not smooth, unless we consider sheaves with special invariants on special surfaces.
For 2 g 6 and 1 n fg, casnati and fontanari cfn have shown that mg. The moduli space of curves is important in both algebraic geometry and geometric topology. Given a collection of geometric objects, and an equivalence relation among them, we would like. The moduli spaces of holomorphic maps elenynicoleta ionel abstract this is a draft of some informal notes that are meant to accompany the second week of the graduate lectures at the 2012 ias women and mathematics program. I will explain how this works and give explicit examples. N2 gauge theories, instanton moduli spaces and geometric.
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