Olav A. Laudal, Gerhard Pfister

Local Moduli and Singularities

• Broschiertes Buch

Produktbeschreibung

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.

---

Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Lecture Notes in Mathematics 1310
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-19235-0
• 1988.
• Seitenzahl: 124
• Erscheinungstermin: 25. Mai 1988
• Englisch
• Abmessung: 235mm x 155mm x 8mm
• Gewicht: 224g
• ISBN-13: 9783540192350
• ISBN-10: 3540192352
• Artikelnr.: 23805470

Inhaltsangabe

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 .