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.


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