Moduli of framed sheaves on projective surfaces

Abstract

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.

13 pages

References in corpus (1)

• The Nekrasov Conjecture for Toric Surfaces

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• Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras
• Topology of moduli spaces of framed sheaves
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• Holomorphic pre-symplectic form on the nested Hilbert scheme $\mbox{Hilb}^{3,4}(\mathbb{C}^2)$