Cohomology gaps for sheaves on threefolds. (English) Zbl 1250.14031

Ballico, Edoardo; Gasparim, Elizabeth

J. Geom. Symmetry Phys. 21, 29-39 (2011).

In the paper under review, the authors study reflexive sheaves \(E\) of rank \(r\geq 2\), on a smooth projective \(n\)-fold with \(n\geq 3\), framed over a smooth, ample, and effective divisor. They show that some values of the cohomology cannot occur, in particular they show that \(h^0(X,E)\neq r-1\). They also discuss numerous examples.

Reviewer: Maria Chiara Brambilla (Ancona)

MSC:

14J60	Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14J30	\(3\)-folds

Keywords:

Framed reflexive sheaves; cohomology invariants