Stable tensors and moduli space of orthogonal sheaves

Abstract

Let X be a smooth projective variety over C. We find the natural notion of semistable orthogonal bundle and construct the moduli space, which we compactify by considering also orthogonal sheaves, i.e. pairs (E,ϕ), where E is a torsion free sheaf on X and ϕis a symmetric nondegenerate (in the open set where E is locally free) bilinear form on E. We also consider special orthogonal sheaves, by adding a trivialization ψof the determinant of E such that det(ϕ)=ψ^2 ; and symplectic sheaves, by considering a form which is skewsymmetric. More generally, we consider semistable tensors, i.e. multilinear forms on a torsion free sheaf, and construct their projective moduli space using GIT.

36 pages, LaTeX2e, Xy-pic (notation made compatible with math.AG/0206277)

References in corpus (1)

• Stable pairs on curves and surfaces

Cited by in corpus (10)

• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• Moduli Spaces for Principal Bundles in Arbitrary Characteristic
• Chamber Structure and Wallcrossing in The ADHM Theory of Curves I
• Global Boundedness for Decorated Sheaves
• Harder-Narasimhan filtration for rank 2 tensors and stable coverings
• Moduli space of principal sheaves over projective varieties
• On the moduli spaces of parabolic symplectic orthogonal bundles on curves
• On the Gieseker Harder-Narasimhan filtration for principal bundles
• A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve
• Reduction of the Semistability Condition for Tensors