A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve

2013/04/12 by Yashonidhi Pandey, Pandey, Yashonidhi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG #msc:14D20 #msc:14D23 #msc:14F22

paper · pdf · doi:10.48550/arxiv.1304.3682

44 pages

arxiv created 2013/09/24 · arxiv updated 2013/09/25

Abstract

Let (V,q) be a vector bundle on a smooth projective curve X together with a quadratic form q: Sym²(V) \ra O_X (respectively symplectic form q: Λ²V \ra O_X). Fixing the degeneracy locus of the quadratic form induced on V/ker(q), we construct a coarse moduli of such objects. Further, we prove semi-stable reduction theorem for equivalence classes of such objects. In particular, the case when degeneracies of q are higher than one is that of principal interest. We also provide a proof of properness of polystable orthogonal bundles without appealing to Bruhat-Tits theory in any characteristic.

Related

• Orthogonal bundles over curves in characteristic two
• Simplicity of tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve
• Line-Bundle-Valued Ternary Quadratic Bundles Over Schemes
• Degeneration of SL(n)-bundles on a reducible curve
• On the essential dimension of symplectic vector bundles over curves