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Semistable sheaves on a two-dimensional quadric and Kronecker modules. (English. Russian original) Zbl 0785.14006
Russ. Acad. Sci., Izv., Math. 40, No. 1, 33-66 (1993); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 56, No. 1, 38-74 (1992).
The paper is devoted to the study of the relation between semistable sheaves on a two-dimensional quadric surface \(P_ 1 \times P_ 1\) that are represented as the cokernel of an injective morphism \(E_ 1 \times \mathbb{C}^ m \to E_ 2 \otimes \mathbb{C}^ n\), where \(E_ 1\) and \(E_ 2\) are exceptional bundles, and semistable Kronecker modules \(\mathbb{C}^ m \otimes \operatorname{Hom}(E_ 1,E_ 2)^*\to \mathbb{C}^ n\). The main results provide the conditions on topological invariants of such sheaves that are sufficient for coincidence of the moduli space of semistable sheaves and the manifold of the corresponding Kronecker modules.

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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