03119nam 2200589 450 99646651140331620220906122140.03-540-39153-310.1007/BFb0078937(CKB)1000000000437495(SSID)ssj0000324477(PQKBManifestationID)12072200(PQKBTitleCode)TC0000324477(PQKBWorkID)10314279(PQKB)10377765(DE-He213)978-3-540-39153-1(MiAaPQ)EBC5592283(Au-PeEL)EBL5592283(OCoLC)1066193856(MiAaPQ)EBC6841958(Au-PeEL)EBL6841958(PPN)155171968(EXLCZ)99100000000043749520220906d1988 uy 0engurnn|008mamaatxtccrLocal moduli and singularities /Olav Arnfinn Laudal, Gerhard Pfister1st ed. 1988.Berlin, Germany :Springer,[1988]©19881 online resource (VIII, 120 p.) Lecture Notes in Mathematics,0075-8434 ;1310Bibliographic Level Mode of Issuance: Monograph3-540-19235-2 The prorepresenting substratum of the formal moduli -- Automorphisms of the formal moduli -- The kodaira-spencer map and its kernel -- Applications to isolated hypersurface singularities -- Plane curve singularities with k*-action -- The generic component of the local moduli suite -- The moduli suite of x 1 5 +x 2 11 .This research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry. It assumes a working knowledge of deformation theory.Lecture Notes in Mathematics,0075-8434 ;1310Moduli theoryModuli theory.516.35Laudal Olav Arnfinn441133Pfister Gerhard1947-MiAaPQMiAaPQMiAaPQBOOK996466511403316Local moduli and singularities1490463UNISA