Current developments in algebraic geometry

by Caporaso, Lucia

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Title Statements

Full title :Current developments in algebraic geometry / edited by Lucia Caporaso [and others].

Summary

"Algebraic geometry is one of the most diverse fields of research in mathematics. It has had an incredible evolution over the past century, with new subfields constantly branching off and spectacular progress in certain directions, and at the same time, with many fundamental unsolved problems still to be tackled. In the spring of 2009 the first main workshop of the MSRI algebraic geometry program served as an introductory panorama of current progress in the field, addressed to both beginners and experts. This volume reflects that spirit, offering expository overviews of the state of the art in many areas of algebraic geometry. Prerequisites are kept to a minimum, making the book accessible to a broad range of mathematicians. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research"--

"1. Introduction Let X c Pr be a smooth projective variety of dimension n over an algebraically closed field k of characteristic zero, and let n : X -" P"+c be a general linear projection. In this note we introduce some new ways of bounding the complexity of the fibers of jr. Our ideas are closely related to the groundbreaking work of John Mather, and we explain a simple proof of his result [1973] bounding the Thom-Boardman invariants of it as a special case"--

Edition Statements

Publication Date:2012.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2012.

The Physical Object

Description:x, 426 pages : : illustrations ; : 24 cm.

Edition Identifiers

ISBN:9780521768252, 052176825X
oclc:ocn778857507
LC Classification:QA564
Dewey Decimal:516.3/5

Fibers of projections and submodules of deformations -- Introduction to birational anabelian geometry -- Periods and moduli -- The Hodge theory of character varieties -- Rigidity properties of Fano varieties -- The Schottky problem -- Interpolation -- Chow groups and derived categories of K3 surfaces -- Geometry of varieties of minimal rational tangents -- Quotients by finite equivalence relations -- Higher-dimensional analogues of K3 surfaces -- Compactifications of moduli of abelian varieties -- The geography of irregular surfaces -- Basic results on irregular varieties via Fourier-Mukai methods -- Algebraic surfaces and hyperbolic geometry.