
Local Moduli and Singularities
Springer (Publisher)
Published on 25. May 1988
Book
Paperback/Softback
VIII, 120 pages
978-3-540-19235-0 (ISBN)
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.
More details
Series
Edition
1988 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 120 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
201 gr
ISBN-13
978-3-540-19235-0 (9783540192350)
DOI
10.1007/BFb0078937
Schweitzer Classification
Content
The prorepresenting substratum of the formal moduli.- Automorphisms of the formal moduli.- The kodaira-spencer map and its kernel.- Applications to isolated hypersurface singularities.- Plane curve singularities with k*-action.- The generic component of the local moduli suite.- The moduli suite of x 1 5 +x 2 11 .