Kodaira-Spencer maps in local algebra /

Kodaira-Spencer maps in local algebra /

Saved in:

Bibliographic Details
Author / Creator:	Herzog, Bernd, 1949-
Imprint:	Berlin ; New York : Springer-Verlag, 1995.
Description:	1 online resource (xvii, 176 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1597 Lecture notes in mathematics (Springer-Verlag) ; 1597.
Subject:	Homotopy theory. Characteristic functions. Singularities (Mathematics) Characteristic functions. Homotopy theory. Singularities (Mathematics)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11070639

Hidden Bibliographic Details
ISBN:	9783540491033 3540491031 9780387587905 038758790X 9783540587903 354058790X
Notes:	Includes bibliographical references (pages 171-172) and indexes. Restrictions unspecified Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 digitized 2010 HathiTrust Digital Library committed to preserve Print version record.
Summary:	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.
Other form:	Print version: Herzog, Bernd, 1949- Kodaira-Spencer maps in local algebra. Berlin ; New York : Springer-Verlag, 1995 038758790X

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.