Herzog, Bernd.
Kodaira-Spencer Maps in Local Algebra [electronic resource] / by Bernd Herzog. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1994. - XVIII, 182 p. online resource. - Lecture Notes in Mathematics, 1597 0075-8434 ; . - Lecture Notes in Mathematics, 1597 .
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.
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.
9783540491033
10.1007/BFb0074026 doi
Mathematics.
Algebra.
Mathematics.
Algebra.
QA150-272
512
Kodaira-Spencer Maps in Local Algebra [electronic resource] / by Bernd Herzog. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1994. - XVIII, 182 p. online resource. - Lecture Notes in Mathematics, 1597 0075-8434 ; . - Lecture Notes in Mathematics, 1597 .
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.
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.
9783540491033
10.1007/BFb0074026 doi
Mathematics.
Algebra.
Mathematics.
Algebra.
QA150-272
512