Lagrangian subbundles of symplectic bundles over a curve

Details Lagrangian subbundles of symplectic bundles over a curve Lagrangian subbundles of symplectic bundles over a curve

2010-12-07

arxiv.org/abs/1012.1538v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

A symplectic bundle over an algebraic curve has a natural invariant $\sLag$ determined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre invariants of a vector bundle. We give a sharp upper bound on $\sLag$ which is analogous to the Hirschowitz bound on the classical Segre invariants. Furthermore, we study the stratifications induced by $\sLag$ on moduli spaces of symplectic bundles, and get a full picture for the case of rank four.

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