Kodaira-Spencer Maps in Local Algebra / Edition 1

by Bernd Herzog

Overview

The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space.

A weakened version of Lech's inequality is proved using a construction that can be considered as a local analog of the Kodaira-Spencer map known from the deformation theory of compact complex manifolds. The methods are quite elementary, and will be of interest for researchers in deformation theory, local singularities and Hilbert functions.

Product Details

ISBN-13:	9783540587903
Publisher:	Springer Berlin Heidelberg
Publication date:	12/27/1994
Series:	Lecture Notes in Mathematics , #1597
Edition description:	1994
Pages:	182
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Ring filtrations.- Basic lemmas.- Tangential flatness under base change.- Relation to flatness.- Distinguished bases.- Hilbert series.- Flatifying filtrations.- Kodaira-Spencer maps.- Inequalities related with flat couples of local rings.- On the local rings of the Hilbert scheme.