Stable sheaves on elliptic fibrations

Abstract

We characterize the subscheme of the moduli space of torsion-free sheaves on an elliptic surface which are stable of relative degree zeero (with respect to a polarization of type aH+bf, H being the section and f the elliptic fibre) which is isomorphic, via the relative Fourier-Mukai transform, with the relative compactified Simpson Jacobian of the family of those curves D in the surface which are flat over the base of the elliptic fibration. This generalizes and completes earlier constructions due to Friedman, Morgan and Witten. We also study the relative moduli scheme of sheaves whose restriction to each fibre is torsion-free and semistable of rank n and degree zero for higher dimensional elliptic fibrations. The relative Fourier-Mukai transform induces an isomorphic between this relative moduli space and the relative n-th symmetric product of the fibration.

AMS-LaTeX, 18 pages, XY-pic; new title, some modifications; final version as accepted in J. Geom. Phys

References in corpus (3)

• Vector Bundles over Elliptic Fibrations
• ICMP lecture on Heterotic/F-theory duality
• The Heterotic String, the Tangent Bundle, and Derived Categories

Cited by in corpus (10)

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• The Spectral Construction for a (1,8)-Polarized Family of Abelian Varieties
• Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves
• T-structures on elliptic fibrations
• A Fourier-Mukai transform for real torus bundles
• Fourier-Mukai transforms for coherent systems on elliptic curves
• Fourier-Mukai partners of singular genus one curves
• Moduli Spaces of Semistable Sheaves on Singular Genus One Curves
• Derived equivalences and Kodaira fibers
• Wall crossing for moduli of stable sheaves on an elliptic surface