Moduli spaces london mathematical society lecture note. We construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following. Youve got multiple files documents, spreadsheets, and email attachments from virtually everyone. In the meantime i would like to join these two pdfs seamlessly. A notion of object and equivalence of objects, a notion of family over a base scheme band equivalence of families, a notion of pullback of families compatible with equivalence.
Combine files into a single pdf, insert a pdf into another pdf, insert a clipboard selection into a pdf, or placeinsert a pdf as a link in another file. From this we induce a onetoone correspondence between these moduli spaces and calculate the dimension of the atwisted. Minicourse on moduli spaces university of michigan. To study many aspects of moduli theory in a simple setting motivates us to begin our exploration with the grassmannian. In mathematics, there are many geometric and topological objects whose points are not actually points zero dimensional object rather they can represent different things. In this case there exist three complex structures i, jand ksatisfying the. C2 moduli space m gof curves of genus gis a projective variety.
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. 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 quantum field theories, the possible vacua are usually labelled by the vacuum expectation values of scalar fields, as lorentz invariance forces the vacuum expectation values of any higher spin fields to vanish. Merge pdf files combine pdfs in the order you want with the easiest pdf merger available. The exact program will depend on the wishes of the participants, but we will start with moduli spaces of elliptic curves and with modular forms, both in a complex analytic and a more algebraic geometric setting. Nevertheless, something is known about the type of singularities they can attain. Curves of genus g, onedimensional subspaces of rn, finite sets. The latter notion is simpler and will be discussed in the next section. Moduli spaces and modular forms universiteit leiden.
Pdf parametrization of the moduli space of hyperelliptic. 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. We suppose that this is a saturated class of morphisms which contains all isomorphisms. Pdf moduli spaces of coherent systems of small slope on. Merge two pdf pages into new one without blank spaces. Some of the main results about compact hyperk ahler. By using pdf2go you can merge pdf documents without having to waste space on your hard drive, ridding you from the fear of viruses and malware from other programs you have to download and install. Moduli spaces of hyperk ahler manifolds and mirror symmetry. Copy the cells you need from excel and paste use ctrl v on keyboard or click mouse in box below to paste. Msri dynamics on moduli spaces of geometric structures. Moduli spaces of sheaves and hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from bridgeland stability conditions and derived category methods. I added a few words outlining other work of harer on the stability of the cohomology of the moduli space of curves. Moduli spaces of higgs bundles in mathematics and physics. Combine or merge files into a single pdf, adobe acrobat dc.
Moduli spaces of metric graphs of genus 1 with marks on. An introduction to moduli spaces of curves and its. Birational geometry of moduli spaces of sheaves and bridgeland stability jack huizenga abstract. Parametrization of the moduli space of hyperelliptic and symmetric riemann surfaces article pdf available in annales academiae scientiarum fennicae mathematica 221 january 1997 with 18 reads.
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. F g, the isotopy classes of orientation preserving di. The moduli space is a quotient of the contractible teichmul. 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 geometric moduli spaces are studied via maps into the period domains. We introduce the moduli space of genus, pointed curves, with enough information.
Symplectic moduli spaces 143 1 irreducible holomorphic symplectic manifolds 1. Moduli spaces are spaces of solutions of geometric classification problems. The most basic problem is that of moduli of smooth complete curves of a fixed genus. How to merge pdfs and combine pdf files adobe acrobat dc. What is a good introductory text for moduli theory. This is precisely what i read when i see the space of vacua for the quantum field theory is a manifold or orbifold, usually called the vacuum manifold. Moduli spaces such as the moduli of elliptic curves which we discuss below play a central role in a variety of areas that have no immediate link to the geometry being classi. Some notes containing a brief survey of the cohomology of the moduli space of curves and the harerzagier formula for the orbifold euler characteristic. More precisely, we show that the spaces m g 1, n v, which parametrize the isometry classes of metric graphs of genus 1 with n marks on vertices are homotopy equivalent to the spaces t m 1, n, which are the moduli spaces of tropical curves of genus 1 with n marked points. 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. The information metric on the moduli space of instantons with global symmetries. Finite group actions on the moduli space of selfdual connections. 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. For example, say the last page of the first pdf file have quite a lot of empty spaces, after merging, i would hope that the second pdf will start from the blank spaces of the first pdf.
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. Sometimes, several pdfs are created when scanning images or a book. In this paper we study homotopy type of certain moduli spaces of metric graphs. Find materials for this course in the pages linked along the left. They have appeared in many subjects of mathematics, from geometry, topology, algebraic geometry to number theory. More precisely, we show that the spaces mgv 1,n, which parametrize the isometry classes of metric graphs of genus 1 with n marks on vertices are homotopy equivalent to the spaces tm1,n, which are the moduli spaces of tropical curves of genus 1 with n marked points. The modern technology is based on rst constructing the stack m g dm, showing that it is coarsely represented by an algebraic space km m g, then nally endowing this space. Introduction hilbert schemes of points moduli of sheaves donaldson invariants curve counting generating functions of invariants of moduli spaces generating functions of invariants of moduli spaces moduli spaces mn depending on n 0. Moduli spaces can be thought of as giving a universal space of parameters for the problem. Follow these steps to use adobe acrobat to combine or merge word, excel, powerpoint, audio, or video files, web pages, or existing pdfs. Moduli spaces of sheaves of rank 2 on a surface are not smooth, unless we consider sheaves with special invariants on special surfaces.
Here different solutions are identified if they are isomorphic that is, geometrically the same. Moduli spaces and formal operads 293 operads in the form that we use in order to generalize them to cyclic and modular operads. Merge all your files word documents, spreadsheets, webpages, images, and more into a single organized pdf thats. The geometry of the moduli space tells you things about the geometry of the spaces points in it. Suppose that we want to classify some kind of object, for example. Its cohomology ring has a elegant structure, and mumford suggested studying the moduli space of curves in the same way. The primary example is the moduli space of elliptic curves. The institute is located at 17 gauss way, on the university of california, berkeley campus, close to grizzly peak, on the. Moduli spaces of metric graphs of genus 1 with marks on vertices. Moduli spaces of coherent systems of small slope on algebraic curves article pdf available in communications in algebra 378 august 2007 with 17 reads how we measure reads. Now youve also got an easy way to combine and organize them all into one pdf. Concerning the geometry of moduli spaces of sheaves of higher rank, there.
Pdf finite group actions on the moduli space of self. In section 5 we prove a characterization of formality of an operad in terms of. On the thick part of the moduli space, there is a positive constant c2, independent of the genus g, such that the sectional curvature k of the weilpetersson metric satis. Good geometry of the moduli spaces of riemann surfaces. One also distinguishes between fine and coarse moduli spaces for the same moduli problem. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. Let cbe a category endowed with a distinguished class of morphism called weak equivalences. Minicourse on moduli spaces emily clader june 2011 1 what is a moduli space. Our aim is to understand the topological nature of. Mcmullen proved that the moduli spaces of riemann surfaces are k.