Local Moduli and SingularitiesThis 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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Contents
INTRODUCTION | 1 |
1 The prorepresenting substratum of the formal moduli | 8 |
2 Automorphisms of the formal moduli | 15 |
Copyright | |
6 other sections not shown
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Common terms and phrases
action Algebraic apply assertion assume Banach Spaces base basis bundle canonical characteristic closed complete complete intersection component compute conics consider construction contains Corollary corresponding cubics curve defined definition denote diagram dimension divisor dual Edited elements embedding equal equation equivalent estimate example exists fact factor fiber Finally finite fixed flat formula function Geometry given gives Hence holds ideal implies induced integral intersection isomorphism Lemma linear locally Mathematics method moduli Moreover morphism multiplicity natural nodal node normal notation Notes obtain ordered pair plane problem Proceedings projective proof Proposition prove pullback rank reduced relations resp restriction satisfies scheme sequence singular smooth space subscheme Suppose surface surjective symmetric tangent Theorem Theory universal variety yields zeros
Bibliographic information
| Title | Local Moduli and Singularities Volume 1310 of Lecture Notes in Mathematics |
| Authors | Olav Arnfinn Laudal, Gerhard Pfister |
| Edition | illustrated |
| Publisher | Springer Berlin Heidelberg, 1988 |
| Original from | the University of California |
| Digitized | Jun 9, 2011 |
| ISBN | 3540192352, 9783540192350 |
| Length | 120 pages |
| Subjects | › › Mathematics / Algebra / General Mathematics / Geometry / Algebraic Mathematics / Group Theory |
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