02864nam 2200661 450 99646637390331620220910014943.03-540-49103-110.1007/BFb0074026(CKB)1000000000437196(SSID)ssj0000324273(PQKBManifestationID)12131564(PQKBTitleCode)TC0000324273(PQKBWorkID)10304908(PQKB)10486362(DE-He213)978-3-540-49103-3(MiAaPQ)EBC5584935(Au-PeEL)EBL5584935(OCoLC)1066197965(MiAaPQ)EBC6842067(Au-PeEL)EBL6842067(OCoLC)793079381(PPN)155229036(EXLCZ)99100000000043719620220910d1994 uy 0engurnn|008mamaatxtccrKodaira-Spencer maps in local algebra /Bernd Herzog1st ed. 1994.Berlin :Springer-Verlag,[1994]©19941 online resource (XVIII, 182 p.) Lecture notes in mathematics ;1597Bibliographic Level Mode of Issuance: Monograph0-387-58790-X 3-540-58790-X Includes bibliographical references and index.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.Lecture notes in mathematics (Springer-Verlag) ;1597.Homotopy theoryCharacteristic functionsSingularities (Mathematics)Homotopy theory.Characteristic functions.Singularities (Mathematics)512.4Herzog Bernd1949-60700MiAaPQMiAaPQMiAaPQBOOK996466373903316Kodaira-Spencer maps in local algebra78123UNISA