Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21850
Brodmann, M; Lashgari, A (2003). A diagonal bound for cohomological postulation numbers of projective schemes. Journal of Algebra, 265(2):631650.

PDF (Preprint)
1MB 
Abstract
Let X be a projective scheme over a field K and let F be a coherent sheaf of OXmodules. We show that the cohomological postulation numbers νFi of F, e.g., the ultimate places at which the cohomological Hilbert functions n dimK (Hi (X, F(n))) =: hFi (n) start to be polynomial for n ≪ 0, are (polynomially) bounded in terms of the cohomology diagonal (hFi (i) i=0dim(F) of F. As a consequence, we obtain that there are only finitely many different cohomological Hilbert functions hFi if F runs through all coherent sheaves of OXmodules with fixed cohomology diagonal. In order to prove these results, we extend the regularity bound of Bayer and Mumford [Computational Algebraic Geometry and Commutative Algebra, Proc. Cortona, 1991, Cambridge Univ. Press, 1993, pp. 148] from graded ideals to graded modules. Moreover, we prove that the CastelnuovoMumford regularity of the dual FV of a coherent sheaf of OℙrK, modules F is (polynomially) bounded in terms of the cohomology diagonal of F. © 2003 Published by Elsevier Inc.
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
DDC:  510 Mathematics 
Uncontrolled Keywords:  Cohomology of projective schemes; Cohomological Hilbert functions; Cohomological postulation numbers; Castelnuovo–Mumford regularity 
Language:  English 
Date:  2003 
Deposited On:  27 May 2010 08:35 
Last Modified:  27 Nov 2013 19:43 
Publisher:  Elsevier 
ISSN:  00218693 
Publisher DOI:  10.1016/S00218693(03)002345 
Citations:  Web of Science®. Times Cited: 7 Google Scholar™ Scopus®. Citation Count: 5 
Users (please log in): suggest update or correction for this item
Repository Staff Only: item control page