✦ LIBER ✦

Subbundles of symplectic and orthogonal vector bundles over curves

✍ Scribed by George H. Hitching

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 135 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200510561

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✦ Synopsis

Abstract

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)

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## Abstract Let ℳ︁(__n__ , __d__ ) be a coprime moduli space of stable vector bundles of rank __n__ ≥ 2 and degree __d__ over a complex irreducible smooth projective curve __X__ of genus __g__ ≥ 2 and ℳ︁~__ξ__~ ⊂ ℳ︁(__n__ , __d__ ) a fixed determinant moduli space. Assuming that the degree __d__ i