Moduli of curves j harris, i morrison pdf alzaytoonah university. There has been a recent surge of interest in moduli spaces of curves, catalysed by. Pdf file or convert a pdf file to docx, jpg, or other file format. This means it can be viewed across multiple devices, regardless of the underlying operating system.
Pseudoembedded moduli of ultrastochastic, discretely bijective hulls and problems in elliptic measure theory z. Note that if such a space exists it can have only one point. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. The main ingredient here is the stable reduction theorem for curves. Torelli groups and geometry of moduli spaces of curves. On the virtual euler characteristics of the moduli spaces. The new yahoopowered ads for adobe pdf service makes it easy to place payperclick ads in your pdf files. External links topology and geometry of the moduli space of curves moduli of stable maps, gromovwitten. I paid for a pro membership specifically to enable this feature.
It is somewhat important to keep in mind that a family of curves is a morphism f. On the virtual euler characteristics of the moduli spaces of. If your pdf reader is displaying an error instead of opening a pdf file, chances are that the file is c. The arithmetic study of the moduli spaces began with jacobis fundamenta nova in 1829, and the modern theory was erected. Mumford, in towards an enumerative geometry of the moduli space of curves publishedin1983,writes.
Moduli of certain wild covers of curves jianru zhang a. The recursion comes from the edge removal operation on the space of ribbon graphs. Intersection theory on moduli spaces of curves via hyperbolic. The moduli spaces of pointed real curves have recently attracted attention in various contexts such as multiple. We already know that curves is an algebraic stack over z, see.
Then v dis the quotient u dautp2 where u dis the open locus of smooth curves in the hilbert scheme h d of plane curves of degree d. Aims theaimofthisbookistoprovideaguidetoarichandfascinatings ject. The past decade has seen substantial progress in understanding the moduli space of curves, involvingideas,forexample,fromgeometryalgebraic,symplectic,anddifferential,physics, topology, and combinatorics. Moduli of certain wild covers of curves jianru zhang. The study of moduli is one of the fundamental aims of algebraic geometry. The moduli space of curves, with applications to enumerative. Gaussian moduli of characteristic, reducible, quasiintegral curves and geometric topology l. Nicole mestrano, carlos simpson hal archive ouverte. An oversized pdf file can be hard to send through email and may not upload onto certain file managers. Deligne products of line bundles over moduli spaces of curves. The perturbed ricci metric that we introduced has bounded. This space parameterizes objects of the form c,p, where cis a hyperelliptic curve of genus gand pis a weierstra. Chaudhuri northwestern university isi bangalore august 1, 20 6 40. How to shrink a pdf file that is too large techwalla.
An absolute moduli problem speaks of parametrizing objects such as varieties themselves, standing alone and not in relation to any xed choices. This is because the satake compactification g of g is projective and the boundary \ has codimension 2. Git constructions of moduli spaces of stable curves and maps. Geometric invariant theory provides a compacti cation v d of v d. Construct two families of segments over a circle that are not equivalent to each other. Let g denote the moduli space of compact riemann surfaces of genus g 3. Consider the moduli problem of isomorphism classes of unit length plane segments up to rigid motion in the plane. Since nefness is a condition that only depends on curves in the space, concretely, this condition can be checked in moduli situations by considering families over a 1dimensional base. There has been a recent surge of interest in moduli spaces of curves, catalysed by the discovery of their connection with string theory. A boundary divisorial basis and its tree representation 27 8. In this paper, the genus of the curves is zero except when the contrary is stated explicitly. The geometry of moduli spaces of pointed curves, the tensor. The singular curve typically has many irreducible components, giving rise to a rich combinatorial structure. The moduli stack of elliptic curves is a smooth separated delignemumford stack of finite type over, but is not a scheme as elliptic curves have nontrivial automorphisms.
A rst guess would be that the moduli space of this problem would be the variety q p 1 p 1 p 1 p nf diagonals g. However, condition 1 says that giving a curve over an algebraically closed. Pdf is a hugely popular format for documents simply because it is independent of the hardware or application used to create that file. Read on to find out just how to combine multiple pdf files on macos and windows 10. We introduce the concepts of moduli spaces, of stable curves and of stable maps in our exposition, and sketch the. The following papers of joe with mumford and eisenbud developed the theory. Giesekers plan for using git to construct the moduli spaces of stable curves, now over 30 years old, has recently been extended to moduli spaces of pointed stable curves and of stable maps by swinarski and baldwin. Git constructions of moduli spaces of stable curves and maps ian morrison abstract. Drinfeld modular forms modulo p and weierstrass points on. We wish to extend the results of 19 to nonnegative, almost countable, nonnegative definite primes. Large sieve with quadratic moduli elliptic curves elliptic curves let p 3 be a prime and let e be an elliptic curve over the eld f p be an elliptic curve given by e.
They have appeared in many subjects of mathematics, from. 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. Adobe designed the portable document format, or pdf, to be a document platform viewable on virtually any modern operating system. Moduli of curves and multiple roots emre can sertoz.
Condition 2 is imposed so that the moduli space is a universal object. It turns out that the class of curves that can arise as limits of smooth curves are curves with only nodal singularities. Zagier department of mathematics, university of maryland, college park, md 20742, usa let fg 1, g 1, be the mapping class group consisting of all isotopy classes of basepoint and. It is known that g is a noncomplete quasiprojective variety that contains many complete curves. Operads and moduli of hyperelliptic curves isi bangalore. Our curves will be connected unless we especially describe them as possibly disconnected. Cimatictp school on moduli of curves, february 29march 4, 2016 in.
Preface aims theaimofthisbookistoprovideaguidetoarichandfascinatingsubject. We show that every essentially markov, quasiprojective, hypereuclidean line is commutative. If your scanner saves files as pdf portbale document format files, the potential exists to merge the individual files into one doc. We denote the corresponding coarse moduli space by m g.
This technique obviously relies on having a robust notion of family of curves, that is, a moduli space. The aim of this paper is to show how facts about the homology of the torelli group imply interesting results about algebraic curves. Chaudhuri mpim operads and moduli of curves 7 august, 2014 5 36. The torelli group tg is the group of isotopy classes of di eomorphisms of a compact orientable surface of genus g that act trivially on the homology of the surface. By richard morochove, pcworld practical it insight from tony bradley todays best tech deals picked by pcworlds editors top deals. Mumford, in towards an enumerative geometry of the moduli space of curves published in 1983, writes. The moduli space of curves and its tautological ring ravi vakil the moduli space of curves has proven itself a central object in geometry. Zagier department of mathematics, university of maryland, college park, md 20742, usa let fg 1, g 1, be the mapping class group consisting of all isotopy classes of basepoint and orientation preserving homeomorphisms of a closed, oriented. 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. The slope stability of the logarithmic cotangent bundle of the dm moduli spaces, chern number inequality and other properties will follow. The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of. Boundary strata in m g,n as customary, we denote by m g,n the moduli stack of stable npointed genus g curves, and by m g,n the corresponding coarse moduli space. The moduli space m g of complete nonsingular curves of genus g admits a compacti cation m g. Deligne products of line bundles over moduli spaces of curves l.
Most electronic documents such as software manuals, hardware manuals and ebooks come in the pdf portable document format file format. Geometry of the moduli space of curves shingtung yau harvard university january, 2007 shingtung yau geometry of the moduli space of curves. We introduce moduli spaces of smooth and stable curves, the tautological cohomology classes on these spaces, and explain how to compute all possible intersection numbers between these classes. As an application we obtain a new proof of the kontsevich constants for the ratio of the euclidean and the symplectic volumes of the moduli space of curves. Boundary strata in m g,n as customary, we denote by m g,n the moduli stack of stable npointed genus g curves, and by m g,n the corresponding coarse moduli.
The moduli space of curves has proven itself a central object in geometry. To combine pdf files into a single pdf document is easier than it looks. Zagier2,3 1 graduate school of mathematics, kyushu university, fukuoka, japan. It turns out that the class of curves that can arise as limits of smooth curves are curves with only nodal singularities and nite automorphism group. A calculus for the moduli space of curves introduction. These curves are moduli spaces for drinfeld modules with level structure, which are the objects which in our setting play a role analogous to that of elliptic curves. Intersection theory on moduli spaces of curves via. We then consider the family of modular curves x 0p constructed by drinfeld, and we study their weierstrass points, a nite set of points of geometric interest. T ur curves by the universal property of the quotient ur, see groupoids in spaces, lemma 22. Chapter 3 contains a discussion of elliptic curves with complex multiplication by the ring of integers of an imaginary quadratic. Tautological and nontautological cohomology of the moduli space of curves pdf.
Therefore, we omit mentioning the genus of the curves. Luckily, there are lots of free and paid tools that can compress a pdf file in just a few easy steps. The authors show indeed in the next chapter that the moduli space can be used to prove results about a single curve. As one would expect intuitively, the taking of limits must be justified, and indeed this is the case here, where. A pdf file is a portable document format file, developed by adobe systems. This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. By smooth curve, we mean a compact also known as proper or complete, smooth also known as nonsingular complex curve, i. The geometry of moduli spaces of pointed curves, the. The moduli space m g of complete nonsingular curves of genus g admits a compacti. The euler characteristic of the moduli space of curves.
Algebraic curves and their moduli cimat guanajuato february. On the kodaira dimension of the moduli space of curves. Geometry of the moduli space of curves ucla mathematics. Thecoarse moduli space of curves of genus g is a scheme m g such that. Searching for a specific type of document on the internet is sometimes like looking for a needle in a haystack. Many of the new ideas are related to the tautological ring. The arithmetic study of the moduli spaces began with jacobis fundamenta nova in 1829, and the modern theory was erected by eichlershimura, igusa, and delignerapoport. The case of the moduli space of curves with genus greater than two is tackled via the potential stability theorem. We want to classify all quadruples in p 1, that is, an ordered set of 4 points which are distinct. In particular its points with values in some field correspond to elliptic curves.
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. The euler characteristic of the moduli space of curves j. The numerical criterion for stability is discussed in detail, with gieseckers criterion given the main focus. The aim of this work is to explore the topological properties of the moduli spaces of pointed real curves. Moduli of curves 3 conversely,letxtbeafamilyofcurves. And to understand the foundation of every step of these. M gc fcrational points of m gg i if n is another scheme such that there is a morphism of functors m g. By michelle rae uy 24 january 2020 knowing how to combine pdf files isnt reserved. These moduli spaces are fundamental objects in algebraic geometry. This article explains what pdfs are, how to open one, all the different ways.
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