A remark on subbundles of symplectic and orthogonal vector bundles over curves

2004/07/19 by George H. Hitching, Hitching, George H.
Mathematics · #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0407323

13 pages; refinement of main result added

arxiv created 2005/09/02 · arxiv updated 2009/12/01

Abstract

We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or orthogonal. We then describe almost all of its rank n vector subbundles using graphs of sheaf homomorphisms, and give criteria for the isotropy of these subbundles.

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