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Local Moduli and Singularities

Olav Arnfinn Laudal, Gerhard Pfister (Autoren)

Buch | Softcover

VIII, 120 Seiten

1988 | 1988
Springer Berlin (Verlag)
978-3-540-19235-0 (ISBN)

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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.

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 .

Erscheint lt. Verlag	25.5.1988
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 120 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	199 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • automorphism • deformation theory • moduli space • Morphismus • Semigroup
ISBN-10	3-540-19235-2 / 3540192352
ISBN-13	978-3-540-19235-0 / 9783540192350
Zustand	Neuware