Kodaira-Spencer maps in local algebra
By: Bernd Herzog.
Series: Lecture notes in mathematics -- 1597
Publisher: Springer-Verlag
Published: 1994
Place of publication: Berlin; London
Language: eng
Number of pages: 176
Subjects: Algebra.; Rings (Algebra); Tensor algebra.; Hilbert algebras.; Artin rings.
Description: 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.
Notes: Includes bibliographical references and index.