Monads for framed torsion-free sheaves on multi-blow-ups of the projective plane

Abstract

We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we construct monads for families of such sheaves parameterized by a noetherian scheme S of finite type. A universal monad on the moduli space is introduced and used to prove that the moduli space is fine.

32 pages

References in corpus (2)

• Moduli of framed sheaves on projective surfaces
• Moduli spaces of framed perverse instantons on P^3

Cited by in corpus (8)

• ADHM construction of perverse instanton sheaves
• Monad constructions of omalous bundles
• Moduli spaces of framed sheaves and quiver varieties
• Hilbert schemes of points of ${\mathcal{O}}_{{\mathbb{P}}^1}(-n)$ as quiver varieties
• Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^n$ at a point
• Holomorphic bundles on the blown-up plane and the bar construction
• ADHM data for the Hilbert scheme of points of the total space of ${\mathcal{O}}_{{\mathbb{P}}^1}(-n)$
• Linear data for framed sheaves via exceptional sequences