Monads for framed sheaves on Hirzebruch surfaces

Abstract

We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.

30 pages. v2: Section 2 partially rewritten. v3: some minor changes and additions. v4: some minor changes, typos corrected. Final version to appear in Adv. Geom. v5: corrects a mistake in a preliminary result in Section 2. All results in Sections 3 to 6 are unchanged

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