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Monday, August 3, 2020 | History

1 edition of Moduli of Curves and Abelian Varieties found in the catalog.

Moduli of Curves and Abelian Varieties

the Dutch Intercity Seminar on Moduli

by Carel Faber

  • 370 Want to read
  • 38 Currently reading

Published by Vieweg+Teubner Verlag in Wiesbaden .
Written in English


Edition Notes

Statementedited by Carel Faber, Eduard Looijenga
SeriesAspects of Mathematics, 0179-2156 -- 33, Aspects of Mathematics -- 33.
ContributionsLooijenga, Eduard
The Physical Object
Format[electronic resource] :
Pagination1 online resource (VIII, 200 pages).
Number of Pages200
ID Numbers
Open LibraryOL27075720M
ISBN 103322901726
ISBN 109783322901729
OCLC/WorldCa840291426

S. Lang, “Abelian Varieties” and it has seemed timely to incorporate them into a new book. We treat exclusively abelian varieties, and do not pretend to write a treatise on algebraic groups. Hence we have summarized in a first chapter all the general results on algebraic groups that are used in the sequel. The theory of moduli, i.e. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

varieties, and its relationship with compactifications of moduli stacks. The standard example considered in this context is the moduli stack M g of genus g curves (where g ≥2) and the Deligne-Mumford compactification M g ⊂M g [9]. The stack M g has many wonderful properties: (1) It has a moduli interpretation as the moduli stack of stable. Introduction The easiest way to understand abelian varieties is as higher-dimensional analogues of ellip-tic curves. Thus we first look at the various definitions of an elliptic curve.

2 Moduli of Elliptic Curves 20 Comparing Abelian Varieties with Strict Abelian Varieties 21 1,1 called the moduli stack of elliptic curves such that, for any commutative ring R, all algebraic constructions we consider in this book should be understood in the “derived” sense. For example, if . Moduli of Curves - Ebook written by Joe Harris, Ian Morrison. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Moduli of Curves.


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Moduli of Curves and Abelian Varieties by Carel Faber Download PDF EPUB FB2

New. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties.

: Moduli of Curves and Abelian Varieties: The Dutch Intercity Seminar On Moduli (Aspects Of Mathematics) (): Faber, Carel: Books. About this book Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics.

Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

The book will appeal to. This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes.

van der Geer G., Oort F. () Moduli of Abelian Varieties: A Short Introduction and Survey. In: Faber C., Looijenga E. (eds) Moduli of Curves and Abelian Varieties. Aspects of Mathematics, vol Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool.

For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for.

Curves and Abelian Varieties About this Title. Valery Alexeev, Arnaud Beauville, C. Herbert Clemens and Elham Izadi, Editors. Publication: Contemporary Mathematics Publication Year Volume ISBNs: (print); (online). Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties.

In this talk, we will discuss basics of moduli space of abelian varieties with additional structures: PEL for polarizations, endomorphisms, and level structure.

We will start with the case of modular curve, then the Siegel space, then move on to the case of unitary Shimura varieties, and nally Hilbert modular varieties. Moduli of Curves and Abelian Varieties: the Dutch Intercity Seminar on Moduli.

[Carel Faber; Eduard Looijenga] -- The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G.

van der Geer, F. Oort and C. Peters. contains a (−2) curve, so there is no modification that gives us a family of smooth curves. Since M g is not complete, a natural question is to ask whether it is affine. The answer again is no.

This follows from the fact that M g has a projective compactification in the moduli space of abelian varieties, such that boundary has codimension 2. Dutch Intercity Seminar on Moduli (). Moduli of curves and abelian varieties.

Braunschweig: Vieweg, © (OCoLC) Material Type: Conference publication, Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: C Faber; E Looijenga. An illustration of an open book. Books. An illustration of two cells of a film strip. Video An illustration of an audio speaker.

Modular curves, Abelian varieties, Moduli theory, Abelian varieties, Modular curves, Moduli theory Publisher ℚ-curves and Abelian Varieties of GL2-type from Dihedral Genus 2 Curves. There is some overlap, e.g. moduli of curves is not in the curves section and moduli of abelian varieties is not in the moduli section.

Following a long tradition in classical geometry (seen clearly in the work of Coxeter), I have always loved finding new and sometimes exotic examples and have collected eight papers of this sort in the Examples.

one could construct compactifications of the moduli spaces at least for curves, abelian varieties and K3 surfaces because they are basic objects in algebraic geometry. As is well known, we have the Deligne-Mumford compactification for curves [DM69], whereas there are quite a lot of compactifications of the moduli of abelian varieties ([AMRT75].

It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and. Logarithmic abelian varieties, III: Logarithmic elliptic curves and modular curves - Volume - Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama.

We illustrate the theory of log abelian varieties and their moduli in the case of log elliptic curves. Send article to Kindle. Lecture 3 (basic material on Jacobians and theta functions) is parallel to Lecture 1 (description of curves); lecture 4 (the relation between the moduli of Abelian varieties and the moduli of curves via the Jacobian, i.e., on the Torelli theorem and the Schottky problem) is parallel to Lecture 2 (the moduli of curves).

by Silvia Brannetti, Margarida Melo, Filippo Viviani - Adv. in Math. (), – Available at arXiv Abstract We construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties, working in the category of (what we call) stacky fans.

We will explore minimal models of curves, rational points on curves, Abelian varieties, isogenies, Honda-Tate theory, Weil descent, applications to isogeny based cryptography, etc. The area is a very active area of research and we expect that the session will be well attended.A complex abelian variety is a smooth projective variety which happens to be a complex torus.

This simpli es many things compared to general varieties, but it also means that one can ask harder questions. Abelian varieties are indeed abelian groups (unlike elliptic curves .Curves, abelian varieties and the Schottky problem Samuel Grushevsky 1 Abelian varieties and their moduli space A g De nitions De nition 1.

An abelian variety is a projective variety which is a group object with holomorphic structure maps. Exercise 1. Any abelian variety is an abelian group.

Example 1. The torus C=(Z+ Z˝) for any ˝2CnR.