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Download or read book Kodaira-Spencer Maps in Local Algebra written by Bernd Herzog and published by Springer. This book was released on 2006-11-14 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.