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Local moduli and singularities

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 fami...

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Detalles Bibliográficos
Autores principales: Laudal, Olav Arnfinn, Pfister, Gerhard
Lenguaje:eng
Publicado: Springer 1988
Materias:
Acceso en línea:https://dx.doi.org/10.1007/BFb0078937
http://cds.cern.ch/record/1691264
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author Laudal, Olav Arnfinn
Pfister, Gerhard
author_facet Laudal, Olav Arnfinn
Pfister, Gerhard
author_sort Laudal, Olav Arnfinn
collection CERN
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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spelling cern-16912642021-04-21T21:11:19Zdoi:10.1007/BFb0078937http://cds.cern.ch/record/1691264engLaudal, Olav ArnfinnPfister, GerhardLocal moduli and singularitiesMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:16912641988
spellingShingle Mathematical Physics and Mathematics
Laudal, Olav Arnfinn
Pfister, Gerhard
Local moduli and singularities
title Local moduli and singularities
title_full Local moduli and singularities
title_fullStr Local moduli and singularities
title_full_unstemmed Local moduli and singularities
title_short Local moduli and singularities
title_sort local moduli and singularities
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BFb0078937
http://cds.cern.ch/record/1691264
work_keys_str_mv AT laudalolavarnfinn localmoduliandsingularities
AT pfistergerhard localmoduliandsingularities