ENGLISH

Local Moduli and Singularities

By Olav Arnfinn Laudal , Gerhard Pfister (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1988
ISBN
3540192352, 9783540192350, 0387192352
DOI
10.1007/BFb0078937
LCC
QA3 .L28 no. 1310,QA564 .L28 no. 1310
Open Library ID
OL2113529M
Language
english
Format
DJVU
Filesize
482 kB (493294 bytes)
Series
Lecture Notes in Mathematics 1310
Edition
1
Pages
120\130
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Algebraic Geometry; Topological GroupsLie Groups

Description

This research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry. It assumes a working knowledge of deformation theory.

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