Verwandte Artikel zu Local Moduli and Singularities (Lecture Notes in Mathematics...

Local Moduli and Singularities (Lecture Notes in Mathematics, 1310, Band 1310)

Laudal, Olav Arnfinn; Pfister, Gerhard

 
9783540192350: Local Moduli and Singularities (Lecture Notes in Mathematics, 1310, Band 1310)
ISBN 10: 3540192352 ISBN 13: 9783540192350
Verlag: Springer Berlin Heidelberg, 2008

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

Die Autoren, Hochschuldozent Dr. Theo de Jong und Prof. Dr. Gerhard Pfister, lehren an den Universitäten Saarbrücken bzw. Kaiserslautern im Fachgebiet Mathematik.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer Berlin Heidelberg
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
3540192352
ISBN 13 
9783540192350
Einband
Broschiert
Anzahl der Seiten
128
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Europaplatz 3
Heidelberg
69115
Deutschland