Abstract:
The author studies the connection between semistable sheaves on $\mathbf P^1\times\mathbf P^1$ that are represented as the cokernel of an injective morphism $E_1\otimes\mathbf C^m\to E_2\otimes\mathbf C^n$, where $E_1$ and $E_2$ are exceptional bundles, and semistable Kronecker modules $\mathbf C^m\otimes\operatorname{Hom}(E_1,E_2)^*\to\mathbf C^n$. He obtains sufficient conditions on the topological invariants of the sheaves for the moduli space of semistable sheaves and the corresponding Kronecker moduli space to coincide. This gives important geometric information concerning the moduli spaces of the bundles.
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