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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spinor bundles on quadrics


Author: Giorgio Ottaviani
Journal: Trans. Amer. Math. Soc. 307 (1988), 301-316
MSC: Primary 14F05; Secondary 14M17
MathSciNet review: 936818
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Abstract: We define some stable vector bundles on the complex quadric hypersurface $ {Q_n}$ of dimension $ n$ as the natural generalization of the universal bundle and the dual of the quotient bundle on $ {Q_4} \simeq \operatorname{Gr} (1,\,3)$. We call them spinor bundles. When $ n = 2k - 1$ there is one spinor bundle of rank $ {2^{k - 1}}$. When $ n = 2k$ there are two spinor bundles of rank $ {2^{k - 1}}$. Their behavior is slightly different according as $ n \equiv 0\;(\bmod 4)$ or $ n \equiv 2\;(\bmod 4)$. As an application, we describe some moduli spaces of rank $ 3$ vector bundles on $ {Q_5}$ and $ {Q_6}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936818-5
PII: S 0002-9947(1988)0936818-5
Keywords: Vector bundle, homogeneous, stable, spinor, moduli space
Article copyright: © Copyright 1988 American Mathematical Society