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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Geometry

• Full title: Local Moduli and Singularities
• Author: Olav A. Laudal, Gerhard Pfister
• Language: English
• Binding: Paperback
• Number of pages: 120
• EAN: 9783540192350
• ISBN: 3540192352
• ID: 01558527
• Publisher: Springer, Berlin
• Weight: 224 g
• Dimensions: 234 × 156 × 6 mm

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