Cohomological invariants of coherent sheaves over projective schemes: A survey. (English) Zbl 1058.14029

Brodmann, Markus

Lyubeznik, Gennady (ed.), Local cohomology and its applications. Selected papers of the international workshop, Guanajuato, Mexico. New York, NY: Marcel Dekker (ISBN 0-8247-0741-9/pbk). Lect. Notes Pure Appl. Math. 226, 91-120 (2002).

Summary: We give a survey on certain results related to the cohomology of projective schemes with coefficients in coherent sheaves. In particular we present results on cohomological patterns, cohomological Hilbert functions and cohomological Hilbert polynomials. Bounding results for Castelnuovo-Mumford regularities, Severi coregularities and cohomological postulation numbers are discussed. Moreover, a number of open questions is presented.
For the entire collection see [Zbl 0974.00036].

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
13D40	Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series

Keywords:

cohomological patterns; cohomological Hilbert functions