LEADER 03119nam 2200589 450 001 996466511403316 005 20220906122140.0 010 $a3-540-39153-3 024 7 $a10.1007/BFb0078937 035 $a(CKB)1000000000437495 035 $a(SSID)ssj0000324477 035 $a(PQKBManifestationID)12072200 035 $a(PQKBTitleCode)TC0000324477 035 $a(PQKBWorkID)10314279 035 $a(PQKB)10377765 035 $a(DE-He213)978-3-540-39153-1 035 $a(MiAaPQ)EBC5592283 035 $a(Au-PeEL)EBL5592283 035 $a(OCoLC)1066193856 035 $a(MiAaPQ)EBC6841958 035 $a(Au-PeEL)EBL6841958 035 $a(PPN)155171968 035 $a(EXLCZ)991000000000437495 100 $a20220906d1988 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLocal moduli and singularities /$fOlav Arnfinn Laudal, Gerhard Pfister 205 $a1st ed. 1988. 210 1$aBerlin, Germany :$cSpringer,$d[1988] 210 4$dİ1988 215 $a1 online resource (VIII, 120 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1310 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-19235-2 327 $aThe 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 . 330 $aThis research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry. It assumes a working knowledge of deformation theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1310 606 $aModuli theory 615 0$aModuli theory. 676 $a516.35 700 $aLaudal$b Olav Arnfinn$0441133 702 $aPfister$b Gerhard$f1947- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466511403316 996 $aLocal moduli and singularities$91490463 997 $aUNISA