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INICIO | 28 de mayo de 2024

Unobstructedness and dimension of families of Gorenstein algebras.

Título inglés Unobstructedness and dimension of families of Gorenstein algebras.
Título español Carencia de obstrucciones y dimensión de familias de álgebras de Gorenstein.
Autor/es Kleppe, Jan O.
Organización Fac. Eng. Oslo Univ. College, Oslo, Noruega
Revista 0010-0757
Publicación 2007, 58 (2): 199-238, 31 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general theorem on deformations of the homogeneous coordinate ring of a scheme Proj(A) which is defined as the degeneracy locus of a regular section of the dual of some sheaf M of rank r supported on say an arithmetically Cohen-Macaulay subscheme Proj(B) of Proj(R). Under certain conditions (notably; M maximally Cohen-Macaulay and Ùr M ≈ KB(t) a twist of the canonical sheaf), then A is Gorenstein, and under additional assumptions, we show the unobstructedness of A and we give an explicit formula for the dimension of any maximal family of Gorenstein quotients of R with fixed Hilbert function obtained by a regular section as above. The theorem also applies to Artinian quotients A.
The case where M itself is a twist of the canonical module (r = 1) was studied in a previous paper, while this paper concentrates on other low rank cases, notably r = 2 and 3. In these cases regular sections of the first Koszul homology module and of normal sheaves to licci schemes (of say codimension 2) lead to Gorenstein quotients (of e.g. codimension 4) whose parameter spaces we examine. Our main applications are for Gorenstein quotients of codimension 4 of R since our assumptions are almost always satisfied in this case. Special attention are paid to arithmetically Gorenstein curves in P5.
Clasificación UNESCO 120101 ; 120106
Palabras clave español Geometría algebraica ; Esquemas ; Parametrización ; Haces ; Algebras conmutativas ; Anillos y módulos de Cohen-Macaulay
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)