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

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

2004-07-19

arxiv.org/abs/math/0407323v3

Mathematics

Algebraic Geometry

13 pages; refinement of main result added

Scientific paper

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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