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INICIO | 03 de marzo de 2024

Castelnuovo-Mumford regularity of products of ideals.

Título inglés Castelnuovo-Mumford regularity of products of ideals.
Título español Regularidad Castelnuovo-Mumford de productos de ideales.
Autor/es Conca, Aldo ; Herzog, Jürgen
Organización Dip. Mat. Univ. Genova, Génova, Italia;Fachb. 6 Math. Univ. GH-Essen, Essen, Alemania
Revista 0010-0757
Publicación 2003, 54 (2): 137-152, 17 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask, for instance, wether the Castelnuovo-Mumford regularity reg(IM) of the product of an ideal I with a module M is bouded by the sum reg(I) + reg(M). In general this is not the case. But we show that it is indeed the case if either dim R/I ≤ 1 or I is generic (in a very precise sense). Further we show that products of ideals of linear forms have always a linear resolution and that the same is true for products of determinantal ideals of a generic Hankel matrix.
Clasificación UNESCO 120105
Palabras clave español Regularidad ; Ideal de operadores
Código MathReviews MR1995137
Código Z-Math Zbl 1074.13004
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)