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Mathematics - Algebra | Kodaira-Spencer Maps in Local Algebra

Kodaira-Spencer Maps in Local Algebra

Series: Lecture Notes in Mathematics, Vol. 1597

Herzog, Bernd

1994, XVIII, 182 p.

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  • About this book

The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space.
A weakened version of Lech's inequality is proved using a construction that can be considered as a local analog of the Kodaira-Spencer map known from the deformation theory of compact complex manifolds. The methods are quite elementary, and will be of interest for researchers in deformation theory, local singularities and Hilbert functions.

Content Level » Research

Keywords » Hilbert series - Kodaira-Spencer map - algebra - deformation germ - flatification - ring filtration

Related subjects » Algebra

Table of contents 

Ring filtrations.- Basic lemmas.- Tangential flatness under base change.- Relation to flatness.- Distinguished bases.- Hilbert series.- Flatifying filtrations.- Kodaira-Spencer maps.- Inequalities related with flat couples of local rings.- On the local rings of the Hilbert scheme.

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