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Field name	Details
Dewey Class	512
Title	Kodaira-Spencer Maps in Local Algebra ([EBook] /) / by Bernd Herzog.
Author	Herzog, Bernd
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1994.
Physical Details	XVIII, 182 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1597
ISBN	9783540491033
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0074026
Links to Related Works	Subject References: Algebra . Mathematics . Authors: Herzog, Bernd . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512 .

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Kodaira-Spencer Maps in Local Algebra

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