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

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.

### 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