Stable pairs on curves and surfaces

Abstract

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded version)

37 pages, LaTeX Version 2.09, MPI-92-093

Cited by in corpus (40)

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• The Moduli of Reducible Vector Bundles
• Moduli of framed sheaves on projective surfaces
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• Spin canonical invariants of 4-manifolds and algebraic surfaces
• Interplay between opers, quantum curves, WKB analysis, and Higgs bundles
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• Uhlenbeck spaces for $A^2$ and affine Lie algebra ${\widehat{sl}}_n$
• Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
• Representability for some moduli stacks of framed sheaves
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• Gauge theoretical Gromov-Witten invariants and virtual fundamental classes
• The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs
• Rank stable instantons over positive definite four manifolds
• The universal Kobayashi-Hitchin correspondence on Hermitian manifolds
• Holomorphic pre-symplectic form on the nested Hilbert scheme $\mbox{Hilb}^{3,4}(\mathbb{C}^2)$
• Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves
• Representations with Weighted Frames and Framed Parabolic Bundles
• Coherent systems and Brill-Noether theory
• Seiberg-Witten Invariants and Rationality of Complex Surfaces
• Stable pairs on elliptic K3 surfaces