Lagrangian subbundles of symplectic bundles over a curve


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Mathematical proceedings of the Cambridge Philosophical Society;153 (2)


Cambridge University Press

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A symplectic bundle over an algebraic curve has a natural invariant s Lag 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 s Lag which is analogous to the Hirschowitz bound on the classical Segre invariants. Furthermore, we study the stratifications induced by s Lag on moduli spaces of symplectic bundles, and get a full picture for the case of rank four



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