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

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

2000-08-25

arxiv.org/abs/math/0008198v1

Mathematics

Algebraic Geometry

38 pages, AMSLaTeX, also available at http://www.math.lsa.umich.edu/~nevins/

Scientific paper

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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