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Kodaira-Spencer Maps in Local Algebra

Kodaira-Spencer Maps in Local Algebra

Paperback

Series: Lecture Notes in Mathematics, Book 1597

Algebra

ISBN10: 354058790X
ISBN13: 9783540587903
Publisher: Springer Nature
Published: Dec 16 1994
Pages: 182
Weight: 0.63
Height: 0.42 Width: 6.14 Depth: 9.21
Language: English
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.

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Algebra