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Typical sheaves of generalized CM-modules


Brodmann, M (1992). Typical sheaves of generalized CM-modules. Manuscripta Mathematica, 76(1):181-192.

Abstract

Let $M$ be a generalized Cohen-Macaulay module over a Noetherian local ring $(R,{\germ m})$. Fix a standard system of parameters $x_1,\cdots, x_d \in {\germ m}$ with respect to $M$ and let $I=\sum^d_{i=1} x_i R$. In this paper, we construct a coherent Cohen-Macaulay sheaf ${\scr K}$ over the projective space ${\bf P}^{d-1}_{R/I}$ whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules $H^i_{\germ m} (M)$ $(i=0,\cdots, d-1)$.

Let $M$ be a generalized Cohen-Macaulay module over a Noetherian local ring $(R,{\germ m})$. Fix a standard system of parameters $x_1,\cdots, x_d \in {\germ m}$ with respect to $M$ and let $I=\sum^d_{i=1} x_i R$. In this paper, we construct a coherent Cohen-Macaulay sheaf ${\scr K}$ over the projective space ${\bf P}^{d-1}_{R/I}$ whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules $H^i_{\germ m} (M)$ $(i=0,\cdots, d-1)$.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:typical sheaf; Cohen-Macaulay module; system of parameters; cohomological Hilbert functions
Language:English
Date:1992
Deposited On:01 Jun 2010 14:20
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0025-2611
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF02567754
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN365956996_0076&DMDID=dmdlog16
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0771.13005

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