When does depth stabilize early on?
| Autor: | Le Dinh Nam, Matteo Varbaro |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Monomial Pure mathematics Algebra and Number Theory Mathematics::Commutative Algebra Polynomial ring 010102 general mathematics Local cohomology Cohomological dimension Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Dimension (vector space) 0103 physical sciences Converse FOS: Mathematics 13A15 13A30 010307 mathematical physics 0101 mathematics Rees algebra Constant (mathematics) Mathematics |
| Popis: | In this paper we study graded ideals I in a polynomial ring S such that the numerical function f(k)=depth(S/I^k) is constant. We show that, if (i) the Rees algebra of I is Cohen-Macaulay, (ii) the cohomological dimension of I is not larger than the projective dimension of S/I and (iii) the K-algebra generated by some generators of I is a direct summand of S, then f(k) is constant. When I is a square-free monomial ideal, the above criterion includes as special cases all the results of a recent paper by Herzog and Vladoiu. In this combinatorial setting there is a chance that the converse of the above fact holds true. Comment: The title has been changed and other minor changes have been done. The paper will appear in Journal of Algebra |
| Databáze: | OpenAIRE |
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