Orthogonal and spin bundles over hyperelliptic curves. (English) Zbl 0541.14012

Ramanan, S.

Proc. Indian Acad. Sci., Math. Sci. 90, 151-166 (1981).

Let \({\mathcal P}\) be a generic pencil of quadrics determined by two quadrics \(Q_ 1\), \(Q_ 2\) of \({\mathbb{P}}^{2g+1}\). To \({\mathcal P}\) is (classically) associated a hyperelliptic curve X of genus g. Let \(M_ d\) be the space of d-dimensional vector subspaces isotropic for both \(Q_ 1\), \(Q_ 2\). The author presents (natural quotients of) the spaces \(M_ d\) as moduli spaces for some classes of orthogonal and spin vector bundles on X.

Reviewer: J.Brun

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14D20	Algebraic moduli problems, moduli of vector bundles
14H10	Families, moduli of curves (algebraic)

Keywords:

orthogonal bundles; spin bundles; hyperelliptic curve associated to pencil of quadrics; moduli spaces

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