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Subbundles of symplectic and orthogonal vector bundles over curves
Author(s) -
Hitching George H.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510561
Subject(s) - mathematics , symplectic geometry , vector bundle , pure mathematics , symplectic vector space , rank (graph theory) , connection (principal bundle) , symplectic representation , moment map , geometry , combinatorics
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 2 n 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. Finally, we sketch the use of these ideas in moduli questions for symplectic vector bundles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)