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Lagrangian subbundles of symplectic bundles over a curve

Published online by Cambridge University Press:  22 February 2012

INSONG CHOE  and
GEORGE H. HITCHING
INSONG CHOE
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Korea. e-mail: [email protected]
GEORGE H. HITCHING
Affiliation:
Høgskolen i Oslo og Akershus, Postboks 4, St. Olavs plass, 0130 Oslo, Norway. e-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 2 , September 2012 , pp. 193 - 214
Copyright
Copyright © Cambridge Philosophical Society 2012

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