Pdf on the geometry of moduli spaces of coherent systems on. For example, the classifying space of rank complex vector. Moduli spaces of hyperk ahler manifolds and mirror symmetry. Create standard compliant pdfs that are compatible with other pdf products. Rational points on moduli spaces of curves by dave jensen. We then turn our attention to the number of different up to diffeomorphism smooth.
Create pdfs with integrated fully functional word, powerpoint, and excel addins. On the compactification of moduli spaces for algebraic k3 surfaces. To study many aspects of moduli theory in a simple setting motivates us to begin. Soda pdf creator online offers a full set of features directly in your web browser. Streamline workflow by converting paper contracts, agreements, and other documents to electronic pdf files.
International max planck research school on moduli spaces. Some notes containing a brief survey of the cohomology of the moduli space of curves and the harerzagier formula for the. Stanford university, department of mathematics, building 380, stanford, california 94305, usa. Zoho creator supports importing data thats present in the following formats. Moduli spaces are spaces of solutions of geometric classification problems. It is part of the bonn international graduate school in mathematics bigsmathematics. Minicourse on moduli spaces university of michigan. We construct the moduli space of contact instantons, an analogue. However, its best you prepare your data by referring to the guidelines.
Nevertheless, something is known about the type of singularities they can attain. Using the simplest methods, and proving as much as possible, formulas are derived for the betti numbers. Francesco scattone this paper is concerned with the problem of describing compact moduli spaces for. In part i we study the hilbert scheme of points of an algebraic variety which is a partial compactification of the configuration space of distinct unordered points.
To appreciate the distinction, show that p1 c is a ne moduli space for one dimensional. Add fillable form fields, such as blank text areas, checkboxes, and multiplechoice questions. R action on moduli space at most tfor the billiard ow on q. In this thesis we study the geometry of two particular moduli spaces. Some of these are online pdf editors that work right in your web browser, so all you have to do is upload your pdf file to the website, make the changes you want, and then save it back to your computer. Observe that a coarse moduli space, if it exists, is unique up to isomorphism. Programma per creare moduli in formato pdf, programma per moduli in pdf, programmi per modificare pdf, software per stampare in pdf, programmi per leggere pdf, stampante virtuale pdf in italiano. Mukai transformation, picard groups of moduli spaces, bundles on the projective plane or.
One also distinguishes between fine and coarse moduli spaces for the same moduli problem. Thats the quick waybut do bear in mind that, typically, an online editor isnt as fully featured as its desktop counterpart, plus the file is exposed to the internet which might be of. An introduction to the moduli spaces of curves by maarten hoeve. Francesco scattone this paper is concerned with the problem of describing compact moduli spaces for algebraic italick3 surfaces of given degree 2italick. Find materials for this course in the pages linked along the left. The corresponding functor is open and bounded matsusakas big theorem, hence there is an algebraic stack m, which is a delignemumford stack if the automorphism group of xis nite. Moduli spaces associated to dynamical systems the geometry of dynamical moduli spaces dynamical moduli spaces further topics dynatomic polynomials and dynamical modular curves canonical heights postcritically finite maps field of moduli and field of definition. The geometric moduli spaces are studied via maps into the period domains.
Inparticular, cohomology classes of the moduli space are universal cohomology classes. Pdfcreator professional enthalt keine werbung wahrend des setups. Minicourse on moduli spaces emily clader june 2011 1 what is a moduli space. The moduli set for objc is the set of equivalence classes with respect to. Given a concrete category c, with objects denoted objc, and an equivalence relation on objc given by morphisms in c. The rough idea is but see the caveat below that the term moduli space is essentially a synonym for representing object and for classifying space. In sections 3 and 4 we introduce these moduli spaces as well as the corresponding period domains. If is a moduli space of a certain kind of object or structure, then facts about can be interpreted as universal statements about all families of such objects. The corresponding functor is open and bounded matsusakas big. Since they occur in different branches of mathematics, the. On the compactification of moduli spaces for algebraic k3.
This online pdf converter can convert all your files to pdf but also compress and merge pdf files. On the geometry of moduli spaces of coherent systems on algebraic curves article pdf available in international journal of mathematics 1804 january 2012 with 37 reads how we measure reads. That is, the points of a moduli space correspond to solutions of geometric problems. On the geometry of moduli spaces of coherent systems on algebraic curves. What is a adobe portable document format adobe reading free at mdeddirectory. Modulispacesofriemannianuj514512020 adobe acrobat reader dcdownload adobe. In part i we study the hilbert scheme of points of an algebraic variety. The most basic problem is that of moduli of smooth complete curves of a fixed genus. Norbert acampo, lizhen ji, and athanase papadopoulos abstract.
Moduli spaces associated to dynamical systems the geometry of dynamical moduli spaces dynamical moduli spaces further topics dynatomic polynomials and dynamical modular curves canonical. Q, and there is a bijection between such maps and families over a1. Pdf some notes containing a brief survey of the cohomology of the moduli space of curves and the harerzagier formula for the orbifold euler characteristic. Browns moduli spaces of curves and the gravity operad core. Browns moduli spaces of curves and the gravity operad. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. An introduction to the topology of the moduli space of stable. An introduction to the topology of the moduli space of. It presents both background information and recent developments on selected topics that. An introduction to moduli spaces of curves and its. Introduction to moduli problems and orbit spaces subject.
Introduction in this talk i will introduce the notions of moduli space and jacobians and briey describe a current research topic. Here different solutions are identified if they are isomorphic that is, geometrically the same. Some of the ideas came from discussions with amir mohammadi. An example of a different kind is the jacobian, which is a moduli space that classi. Professorpnewsteadliverpool,professorlbrambilapazcimat,mexico. The aim of the conference is to bring together researchers interested in moduli spaces of geometric, analytic or algebraic structures. In general, the moduli space m g for a surface f g of genus g is a complicated object. For example, a curve in the moduli space might be a map a1. Pdf parametrization of the moduli space of flat sl2, r. Moduli spaces of sheaves of rank 2 on a surface are not smooth, unless we consider sheaves with special invariants on special surfaces. Our report has a historical character, but the stress is on the chain of mathematical ideas. Concerning the geometry of moduli spaces of sheaves of higher rank, there. Pdf on the geometry of moduli spaces of coherent systems.
Moduli spaces we consider the moduli problem for fano complex manifolds, i. The role of automorphisms on the curves as an obstruction to the. Easily choose the plan that matches your requirements. The free version of pdf architect already allows you to view, rotate, delete and rearrange pages as well as merge multiple documents. This thesis explores the intersection theory on mg,n, the moduli space of genus g stable curves.
Geometry and quantization of moduli spaces springerlink. One can consider moduli spaces of vector bundles, coherent sheaves, etc. The international max planck research school on moduli spaces imprs is the graduate program of the max planck institute for mathematics in bonn mpim jointly offered with the university of bonn. We proceed to explicitly compute the homeomorphism types that arise from nonsmooth moduli spaces of pentagons. Introduction to riemann surfaces, moduli spaces and its applications. Moduli spaces of hyperk ahler manifolds and mirror symmetry 189 1 introduction let m. Pdfcreator allows you to convert files to pdf, merge and rearrange pdf files, create digital signatures and more. Create pdf files,create pdf documents foxit reader. In algebraic geometry, a moduli space of algebraic curves is a geometric space typically a scheme or an algebraic stack whose points represent isomorphism classes of algebraic curves. We then turn our attention to the number of different up to diffeomorphism smooth manifolds that can arise as moduli spaces of polygons. We study the irreducible components of the moduli space of instanton sheaves on \mathbbp3, that is rank 2 torsion free sheaves e. Masur mas2 mas3, there exist c1 and c2 depending on qsuch that for all t1. Soda pdf free online pdf creator create pdf online. Since they occur in different branches of mathematics, the techniques tend to differ, but there are nevertheless unifying questions, and solutions crossing borders.
Moduli spaces london mathematical society lecture note. Pdf architect is the affordable alternative to expensive pdf software. Parametrization of the moduli space of flat sl2, r connections on the torus article pdf available in letters in mathematical physics 593 may 2001 with 63 reads how we measure reads. The study of moduli spaces is an old branch of algebraic geometry with. 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.
We introduce the moduli space of genus, pointed curves, with enough information. The moduli space of curves and its tautological ring by ravi vakil in the notices of the ams. Moduli spaces play a central role in algebraic geometry. With acrobat reader dc you can do more than just open and.
Graduate thesis or dissertation on the topologies of moduli. Word, excel, powerpoint, images and any other kind of document can be easily converted to pdf on. Let denote a generator of the maximal ideal of r and consider the affine plane. The names and logo designs referred to in this sample artwork are fictional and not intended to refer to any actual organization, products or services. There are at least three good reasons to study moduli spaces of sheaves on surfaces.
The conference can be a plattform for the productive exchange of ideas. On the kodaira dimension of the moduli space of curves. Modulispacesofriemannianuj514512020 adobe acrobat reader. The necoarse moduli spaces are endowed with a scheme structure and carry more subtle information than the underlying set parameterizing the geometric objects. The irreducibility of the space of curves of given genus numdam. Moduli spaces ofriemannianuj514512020 adobe acrobat reader dcdownload adobe acrobat reader dc ebook pdf. Email your form or embed it on your website so users can fill it out on their laptops, desktops, cell. We survey some major contributions to riemanns moduli space and teichmu. S1 the moduli space is the upper halfplane h divided by the action of the group sl 2z of m. Moduli spaces of rank 2 instanton sheaves on the projective space. Some of the main results about compact hyperk ahler. Our aim is to understand the topological nature of. It is known that, for a fixed number of edges, this number is finite.
Suppose that we want to classify some kind of object, for example. 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. As for somewhat informal and mostly brief introductions to moduli spaces, see. The following papers of joe with mumford and eisenbud developed the theory. People tend to say classifying space when in the context of topology, and they tend to say moduli space when in a context of complex geometry or algebraic geometry. The role of automorphisms on the curves as an obstruction to the existence of fine moduli spaces is outlined, as well as approaches to deal with these automorphims, particularly the role of marked points. With jotforms fillable pdf form creator, you can create customized pdf forms that users can easily fill out and submit from their digital devices.
Its cohomology ring has a elegant structure, and mumford suggested studying the moduli space of curves in the same way. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. Ingeometryoneusuallywantstodefineinvariantsof thespaces,orgeometricobjects,underconsideration. Moduli spaces can be thought of as giving a universal space of parameters for the problem. With the pdf unlock tool you can easily unlock your protected pdf files and remove the printing, copying and editing lock. The primary example is the moduli space of elliptic curves. The authors first study the case of genus 1 elliptic curves to illustrate the difficulties involved in constructing fine moduli spaces.
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