Author | Laudal, Olav Arnfinn. author |
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Title | Local Moduli and Singularities [electronic resource] / by Olav Arnfinn Laudal, Gerhard Pfister |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1988 |

Connect to | http://dx.doi.org/10.1007/BFb0078937 |

Descript | VIII, 120 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Algebraic geometry
Topological groups
Lie groups
Mathematics
Algebraic Geometry
Topological Groups Lie Groups