These are notes for a series of five lectures on moduli and degenerations of algebraic curves via tropical geometry. Thus it is natural to ask how the curvatures vary in terms of g. It includes workflow manager watchfolder application, configuration manager and the virtual printer scripting tools. The third homology group of the moduli space of curves.
Lectures on tropical curves and their moduli spaces. Arithmetic moduli of elliptic curves katz, nicholas m mazur, barry download bok. Lectures on the moduli stack of vector bundles on a curve. Dec 20, 20 download smartcurve an adobe photoshop plugin that targets users who are looking for a simple solution to modify the curves inside an rgb or gray image. Moduli of curves joe harris, ian morrison download. Its 100% freeware to help you to batch create a set of professional pdfs with djvu files at the same time. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. Then in the last chapter they show the reverse, that the properties of various moduli spaces can be proven using the techniques introduced in the book, such as the irreducibility of the moduli space, the diaz result that complete subvarieties of the moduli space have dimension at most genus 2, and moduli of hyperelliptic curves and severi. Plane curves offer a rich and to some extent unexplored field of study which may be approached from a quite elementary level. The tautological ring of the moduli space of curves. The aim of the course was to use this example to introduce the notion of algebraic stacks and to illustrate how. There will be a preliminary discussion on thursday, 22. Using dedol, we then obtain that the obstruction to the field of moduli k of a curve x of genus g 2 being a field of definition lies in the second cohomological. 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.
Boxoft free djvu to pdf freeware freeware for convert. The moduli space of curves and its tautological ring. Moduli spaces and teichmuller spaces of riemann surfaces have been studied for many. What objects do the cusps of modular curve classify. Let us call the closures of these strata the 1curves. For a more detailed but still informal introduction, see mirsym, part 4. Finally, we describe some of what is known about the tautological ring. From such foundations, the book goes on to show how moduli spaces of curves are constructed, to illustrate typical applications with the proofs of the brillnoether and gieseker petri theorems via limit linear series, and to survey the most important results about their geometry ranging from irreducibility and complete subvarieties to ample. In dimension one, exactly one factor in the product of moduli spaces is m0. The weilpetersson volume grows exponentially in g see also 23, in particular, a rational multiple of. Using the method of algebraic stacks, we can prove not only the irreducibility of mg itself, but of all higher level moduli spaces of curves too cf. As others mentioned, delignerapoports compactified moduli problems are described using the notion of generalized elliptic curve, which is a flat proper family of connected curves of arithmetic genus 1 and at most nodal singularities, equipped with a distinguished section and a group law.
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. Fields medalist maryam mirzakhani, former member in the school of mathematics, gives the first of three 2012 marston morse lectures on dynamics on the moduli spaces of curves. The moduli space m g of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Moduli of curves graduate texts in mathematics 187 9780387984292. We introduce the moduli space of genus, pointed curves, with enough information to give a feel for its basic geography. Lectures on the moduli stack of vector bundles on a curve jochen heinloth preliminary version, january 29, 2009 abstract. The tautological ring of the moduli space of curves m g is a subring rm g of the chow ring am g.
Document express with djvu enterprise edition is the solution for highvolume batch djvu conversion needs. Q, and there is a bijection between such maps and families over a1. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Towards an enumerative geometry of the moduli space of curves, in the. The moduli space of curves alessio corti october 27, 1997 this is a write up of my lecture in the cambridge \geometry seminar, an introduction to the construction and proof that the compacti ed moduli space m gof curves of genus gis a projective variety. The codimensiontwo homology of the moduli space of stable curves. Jholomorphic curves and symplectic topology dusa mcduff.
Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics e. Plane curves, rational points on plane curves, the group law on a cubic curve, functions on algebraic curves and the riemannroch theorem, reduction of an elliptic curve modulo p, elliptic curves over qp, torsion points, neron models, elliptic curves over the complex numbers, the mordellweil theorem. Sample files are included and must be used for demo mode. Geometry of the moduli space of curves shingtung yau harvard university january, 2007 shingtung yau geometry of the moduli space of curves. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. In this paper we compute the asymptotics of the natural metric on the line bundle over the moduli space. Curve3 also has a new demo mode which allows users to test the interface as well as the main calibration and verification functionalities of curve3 including verify mode without a serial number. Here the n marked points and the anchor points of the r tangent vectors are distinct. Aims theaimofthisbookistoprovideaguidetoarichandfascinatings ject. A starting point could be verras article rational parametrizations of moduli spaces of curves.
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. Download smartcurve an adobe photoshop plugin that targets users who are looking for a simple solution to modify the curves inside an rgb or gray image. The complex analytic structure and the relation to teichmuller space is further discussed in. These are not updated notes from the lectures i gave. These are lecture notes of a short course on the moduli stack of vector bundles on an algebraic curve. An introduction to moduli spaces of curves and its. This is the problem underlying siegel modular form theory. To begin with let us restrict ourselves to the field. The codimensiontwo homology of the moduli space of stable curves is algebraic. One can also enrich the problem by considering the moduli stack of genus g nodal curves with n marked points, pairwise distinct and distinct from the nodes. Denote the moduli stack over specz of smooth elliptic curves with n marked points and r nonzero tangent vectors by m1. Fermats method of descent, plane curves, the degree of a morphism, riemannroch space, weierstrass equations, the group law, the invariant differential, formal groups, elliptic curves over local fields, kummer theory, mordellweil, dual isogenies and the weil pairing, galois cohomology, descent by cyclic isogeny. N is a ne moduli space for the moduli problem of nite sets up to bijection. We next introduce the tautological cohomology or chow classes.
They have appeared in many subjects of mathematics, from. Advances in moduli theory yuji shimizu and kenji ueno. Narasimhan, on the cohomologygroups of modulispaces of vector bundles on curves. Curves software free download curves top 4 download. We study the geometry of the moduli stack of vector bundles of.
For example, a curve in the moduli space might be a map a1. The perturbed ricci metric that we introduced has bounded. Minicourse on moduli spaces university of michigan. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in. Dynamics on the moduli spaces of curves i institute for. The past decade has seen substantial progress in understanding the moduli space of curves, involvingideas,forexample,fromgeometryalgebraic,symplectic,anddifferential,physics, topology, and combinatorics. Riemann defined a riemann surface of an algebraic function field as a branched covering of a onedimensional complex projective space, and found out that riemann surfaces have parameters.
Seminar on moduli of curves universitat des saarlandes. Moduli of curves 3 conversely,letxtbeafamilyofcurves. For instance, the higherdimensional analogue of the moduli space of elliptic curves discussed above is the moduli space of abelian varieties, such as the siegel modular variety. Don zagier, john harer, the euler characteristic of the moduli space of curves, inventiones mathematicae 1986 volume.
Besides the boundary divisors, we have the divisor classes i c1li, where li is the line bundle with ber the cotangent space to cat xi, and, the rst chern class of the hodge bundle e of rank g. In higher dimensions, moduli of algebraic varieties are more difficult to construct and study. Boxoft djvu to pdf converter could be the best choice. Knudsen established the existence of a projective moduli space for stable curves. Top 4 download periodically updates software information of curves full versions from the publishers, but some information may be slightly outofdate using warez version, crack, warez passwords, patches, serial numbers, registration codes, key generator, pirate key, keymaker or keygen for curves license key is illegal. For excellent summaries of recent research, see hl, fl. Preface aims theaimofthisbookistoprovideaguidetoarichandfascinatingsubject. Geometry of moduli stacks of k,lstable vector bundles over algebraic curves o.
Mumford and deligne 1 introduced the concept of stable curve in their proof of the irreducibility of the moduli space of curves of genus g. Download curves this adobe photoshop plugin allows you to manipulate an image by choosing from eight curves. Finding ebooks booklid booklid download ebooks for free. The orbifold euler characteristic of the moduli space of curves was originally computed in. Other readers will always be interested in your opinion of the books youve read. The moduli space of curves and its tautological ring ravi vakil the moduli space of curves has proven itself a central object in geometry. T ur curves by the universal property of the quotient ur, see groupoids in spaces, lemma 22. By associating to a curve c and a g d 1 the socalled trace curve and reduced trace curve we define two rational maps. Download for offline reading, highlight, bookmark or take notes while you read moduli of curves. Stanford university, department of mathematics, building 380, stanford, california 94305, usa.
Arithmetic moduli of elliptic curves katz, nicholas m. The modern technology is based on rst constructing the stack m g dm. Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. Get your kindle here, or download a free kindle reading app. The moduli space of npointed genus g curves we next apply the machinery of moduli spaces to algebraic curves. In this seminar, we will read selected articles of the handbook of moduli. Download links are directly from our mirrors or publishers website. Modulistacks for bundles on semistable curves springerlink.
Top 4 download periodically updates software information of curves full versions from the publishers, but some information may be slightly out of date using warez version, crack, warez passwords, patches, serial numbers, registration codes, key generator, pirate key, keymaker or keygen for curves license key is illegal. On fields of moduli of curves 43 using dedol, we then obtain that the obstruction to the field of moduli k of a curve x of genus g 2 being a field of definition lies in the second cohomological group h2k, zautx with values in the center of the automorphism group of x and for a certain action of the. Such marked curves are said to be stable if the subgroup of curve automorphisms which fix the marked points is finite. Derived categories of moduli spaces of vector bundles on. Rational correspondences between moduli spaces of curves.