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- catalog abstract "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.".
- catalog contributor b2130440.
- catalog contributor b2130441.
- catalog contributor b2130442.
- catalog created "c1988.".
- catalog date "1988".
- catalog date "c1988.".
- catalog dateCopyrighted "c1988.".
- catalog description "Bibliography: p. [115]-116.".
- catalog description "Contents: Introduction -- The prorepresenting substratum of the formal moduli -- Automorphismus 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 x15+x211 -- An algorithm to compute the kernel of the Kodaira-Spencer map for an irreducible plane curve singularity -- Bibliography -- Subject Index.".
- catalog 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.".
- catalog extent "v, 116 p. ;".
- catalog hasFormat "Local moduli and singularities.".
- catalog identifier "0387192352 (U.S.)".
- catalog identifier "3540192352".
- catalog isFormatOf "Local moduli and singularities.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1310.".
- catalog isPartOf "Lecture notes in mathematics ; 1310".
- catalog issued "1988".
- catalog issued "c1988.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Local moduli and singularities.".
- catalog subject "Geometry, Algebraic.".
- catalog subject "Mathematics.".
- catalog subject "Moduli theory.".
- catalog subject "QA3 .L28 no. 1310".
- catalog subject "Singularities (Mathematics)".
- catalog subject "Topological Groups.".
- catalog tableOfContents "Contents: Introduction -- The prorepresenting substratum of the formal moduli -- Automorphismus 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 x15+x211 -- An algorithm to compute the kernel of the Kodaira-Spencer map for an irreducible plane curve singularity -- Bibliography -- Subject Index.".
- catalog title "Local moduli and singularities / Olav Arnfinn Laudal, Gerhard Pfister.".
- catalog type "text".