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Record Nr. |
UNISA996466511403316 |
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Autore |
Laudal Olav Arnfinn |
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Titolo |
Local moduli and singularities / / Olav Arnfinn Laudal, Gerhard Pfister |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer, , [1988] |
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©1988 |
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ISBN |
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Edizione |
[1st ed. 1988.] |
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Descrizione fisica |
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1 online resource (VIII, 120 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1310 |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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 . |
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Sommario/riassunto |
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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. |
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