Moduli of framed sheaves on projective surfaces

Details Moduli of framed sheaves on projective surfaces Moduli of framed sheaves on projective surfaces

2009-06-08

arxiv.org/abs/0906.1436v2

Doc. Math. 16 (2011) 399-410

Mathematics

Algebraic Geometry

13 pages

Scientific paper

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of Huybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.

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