Download Curves and Abelian Varieties: International Conference March by Valery Alexeev, Arnaud Beauville, C. Herbert Clemens, Elham PDF

By Valery Alexeev, Arnaud Beauville, C. Herbert Clemens, Elham Izadi

This ebook is dedicated to contemporary development within the research of curves and abelian forms. It discusses either classical facets of this deep and gorgeous topic in addition to very important new advancements, tropical geometry and the speculation of log schemes. as well as unique study articles, this publication includes 3 surveys dedicated to singularities of theta divisors, of compactified Jacobians of singular curves, and of ""strange duality"" between moduli areas of vector bundles on algebraic types

Show description

Read or Download Curves and Abelian Varieties: International Conference March 30-april 2, 2007 University of Georgia Athens, Georgia PDF

Similar algebraic geometry books

Quadratic and hermitian forms over rings

This publication offers the speculation of quadratic and hermitian varieties over jewelry in a truly normal surroundings. It avoids, so far as attainable, any restrict at the attribute and takes complete good thing about the functorial homes of the idea. it's not an encyclopedic survey. It stresses the algebraic points of the idea and avoids - is reasonably overlapping with different books on quadratic types (like these of Lam, Milnor-Husemöller and Scharlau).

Liaison, Schottky Problem and Invariant Theory: Remembering Federico Gaeta

This quantity is a homage to the reminiscence of the Spanish mathematician Federico Gaeta (1923-2007). except a historic presentation of his lifestyles and interplay with the classical Italian tuition of algebraic geometry, the quantity offers surveys and unique learn papers at the arithmetic he studied.

Automorphisms in Birational and Affine Geometry: Levico Terme, Italy, October 2012

The main target of this quantity is at the challenge of describing the automorphism teams of affine and projective forms, a classical topic in algebraic geometry the place, in either situations, the automorphism staff is usually countless dimensional. the gathering covers quite a lot of themes and is meant for researchers within the fields of classical algebraic geometry and birational geometry (Cremona teams) in addition to affine geometry with an emphasis on algebraic team activities and automorphism teams.

Extra resources for Curves and Abelian Varieties: International Conference March 30-april 2, 2007 University of Georgia Athens, Georgia

Sample text

If ~ < fl < 1, we may also write E(vls,/) = E(vls~;) + E(Vls,~\s;). Since the energy of ue on S'~ \ S'~ again is bounded from below by the corresponding one of v up to some additive constant c4, we obtain from the energy minimizing property of u~ E(~I~,) _< E(v~ls~,) + ~, with c5 independent of 5 (but not of r]). Thus, the energy of u~ on S~ for fixed 7] > 5 is bounded independently of ~. Therefore, as d --~ 0, some subsequence of u~ converges on S~' to a harmonic map, using standard estimates for harmonic maps (see [H3]).

2 Let Y be a complete, simply connected, locally compact space of nonpositive curvature with isometry group I(Y). Let F be a group, p : P -+ I(Y) a homomorphism. e. is not contained in a parabolic subgroup of the isometry group of Z'. In geometric terms, this means t h a t there does not exist an unbounded sequence (Yn)neN C Z' with dist(yn, 7(Yn)) --< C(7) for all 7 E p(F), with a constant depending on y, but not on n. Note that any semisimple representation is reductive. For simplicity of notation, we shall consider u in the sequel as a m a p from X into N := y / p ( ~ l ( x ) ) , although N may be singular.

Since u has finite energy, almost all such restrictions need to have finite energy, and as in [JY2, p. 302] we then see that in fact all of them do. Case 1. Suppose that z0 C D ~ lies in the smooth part of Do~. Therefore, estimates for u follow from estimates for finite energy harmonic maps h: D*-+ N where D* -- {z C C : 0 < [z I < 1} is the punctured uinit disk, and N is a R i e m mannian manifold of nonpositive sectional curvature. In the sequel, D* will always be equipped with the Euclidean metric of C, and (r, 9~) will be standard polar coordinates.

Download PDF sample

Rated 4.33 of 5 – based on 15 votes