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Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves

Thomas A. Nevins
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Abstract

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group ${\mathbf C}^*$, and we determine its fixed-point set, which leads in some special cases to explicit formulas for the rational homology of the moduli space.

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Thomas A. Nevins. 2000-08-25. Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves. https://arxiv.org/abs/math/0008198

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