Spinor bundles on quadrics
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- by Giorgio Ottaviani
- Trans. Amer. Math. Soc. 307 (1988), 301-316
- DOI: https://doi.org/10.1090/S0002-9947-1988-0936818-5
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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 ${Q_6}$.References
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Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 307 (1988), 301-316
- MSC: Primary 14F05; Secondary 14M17
- DOI: https://doi.org/10.1090/S0002-9947-1988-0936818-5
- MathSciNet review: 936818