Gaps in Chern classes of rank 2 stable reflexive sheaves
The paper contains the characterization of the set of integers \(c_ 1\), \(c_ 2\), \(c_ 3\) such that there is a rank 2 stable reflexive sheaf on \({\mathbb{P}}^ 3\) whose Chern classes are \(c_ 1\), \(c_ 2\), \(c_ 3\). This answers a question of \textit{R. Hartshorne} [Math. Ann. 254, 121-176 (1980; Zbl 0431.14004)]. The proof consists of two parts. First of all, using the well known correspondence between curves of \({\mathbb{P}}^ 3\) and rank 2 reflexive sheaves, we construct some families of rank 2 reflexive sheaves and we analyse which values of \(c_ 1\), \(c_ 2\), \(c_ 3\) appear. Then we prove that the undecided cases are indeed non-existent.
rank 2 stable reflexive sheaf with prescribed Chern classes
scientific article; zbMATH DE number 3849395