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Moduli of orthogonal and spin bundles over hyperelliptic curves. (English) Zbl 0539.14011
Let i denote the hyperelliptic involution on an irreducible smooth hyperelliptic curve X of genus \(\geq 2\). An i action on a bundle E over X is a map \(j:E\to i^*E\) such that \(i^*j{\mathbb{O}}j=Id.\) Let J be a fixed topological \({\mathcal O}(n)\) bundle with i-action. E is said to be of local type J if E is topologically i-isomorphic to E. By constructing vector spaces, non-degenerate quadratic forms and orthogonal group actions at each Weierstraß point and then taking a direct sum over all Weierstraß points one obtains by quotienting out the group action the space of equivalence classes of semistable orthogonal bundles of rank n with i-action (compatible with orthogonal structure) of a fixed allowable local type J. Relations are made to pencils of quadrics. The results are extended to Clifford bundles.
Reviewer: P.Cherenack

MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14H55 Riemann surfaces; Weierstrass points; gap sequences
14L30 Group actions on varieties or schemes (quotients)
14D20 Algebraic moduli problems, moduli of vector bundles
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