Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14F05, 14M17

Retrieve articles in all journals with MSC: 14F05, 14M17

Additional Information

Keywords: Vector bundle, homogeneous, stable, spinor, moduli space
Article copyright: © Copyright 1988 American Mathematical Society