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

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14D20 Algebraic moduli problems, moduli of vector bundles
14H10 Families, moduli of curves (algebraic)
Full Text: DOI
[1] Usha V Desale and Ramanan S 1976 Classification of vector bundles of rank 2 on hyperelliptic curves;Inventiones Math. 38 161–185 · Zbl 0323.14012 · doi:10.1007/BF01408570
[2] Luc Gauthier 1954-55 Footnote to a footnote of AndrĂ© Weil.Univ. de Politec. Turino Rend. Sem. Math. 14 325–328.
[3] Mumford D 1965Geometric invariant theory, (Springer-Verlag)
[4] Narasimhan M S and Ramanan S 1975 Generalised Prym varieties as fixed points;J. Indian Math. Soc. p. 1–19 · Zbl 0422.14018
[5] Ramanathan A, Stable principal bundles on a compact Riemann surface, Springer Lecture Notes (to appear) · Zbl 0284.32019
[6] Reid MIntersection of two or more quadrics, Thesis, Cambridge
[7] Serre J PCohomologie Galoisienne, (Paris: Hermann)
[8] Seshadri C S 1967 Space of unitary vector bundles on a compact Riemann surface;Ann. Math. 85 303–336. · Zbl 0173.23001 · doi:10.2307/1970444
[9] A Weil 1954 Footnote to a recent paper;Am. J. Math. 76 347–350 · Zbl 0056.03702 · doi:10.2307/2372576
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