Bounds for the regularity of local cohomology of bigraded modules
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  • 作者:Jürgen Herzog (1)
    Ahad Rahimi (2) (3)
  • 关键词:The Castelnuov ; Mumford regularity ; Local cohomology ; Free resolution ; Mutigraded modules ; 13D45 ; 13D02 ; 16W50
  • 刊名:Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 出版年:2014
  • 出版时间:March 2014
  • 年:2014
  • 卷:55
  • 期:1
  • 页码:289-300
  • 全文大小:172 KB
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    3. Borna, K., Rahimi, A., Rasolyar, S.: Relative Buchsbaumness of bigraded modules. Colloq. Math. 127, 161-72 (2012) CrossRef
    4. Eisenbud, D.: Commutative Algebra with a View to Algebraic Geometry. Springer, Berlin (1995)
    5. Rahimi, A.: On the regularity of local cohomology of bigraded algebras. J. Algebra 302, 313-39 (2006) CrossRef
    6. Rahimi, A.: Tameness of local cohomology of monomial ideals with respect to monomial prime ideals. J. Pure Appl. Algebra 211, 83-3 (2007)
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    8. Rahimi, A.: Sequentially Cohen-Macaulay modules with respect to an irrelevant ideal. arXiv: 1112. 3717 (2012)
  • 作者单位:Jürgen Herzog (1)
    Ahad Rahimi (2) (3)

    1. Fachbereich Mathematik, Universit?t Duisburg-Essen, Campus Essen, 45117, Essen, Germany
    2. Department of Mathematics, Razi University, Kermanshah, Iran
    3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
  • ISSN:2191-0383
文摘
Let $M$ be a finitely generated bigraded module over the standard bigraded polynomial ring $S=K[x_1,\ldots ,x_m, y_1,\ldots ,y_n]$ , and let $Q=(y_1,\ldots ,y_n)$ . The local cohomology modules $H^k_Q(M)$ are naturally bigraded, and the components $H^k_Q(M)_j=\bigoplus _iH^k_Q(M)_{(i,j)}$ are finitely generated graded $K[x_1,\ldots ,x_m]$ -modules. In this paper we study the regularity of $H^k_Q(M)_j$ , and show in several cases that $\mathrm reg H^k_Q(M)_j$ is linearly bounded as a function of $j$ .

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