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Torus-equivariant vector bundles on projective spaces

Published online by Cambridge University Press:  22 January 2016

Tamafumi Kaneyama
Tamafumi Kaneyama*
Affiliation:
Department of Mathematics, Gifu College of Education, Yanaizu-cho Hashima-gun, Gifu 501-61, Japan
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For a free Z-module N of rank n, let T = TN be an n-dimensional algebraic torus over an algebraically closed field k defined by N. Let X = TN emb (Δ) be a smooth complete toric variety defined by a fan Δ (cf. [6]). Then T acts algebraically on X. A vector bundle E on X is said to be an equivariant vector bundle, if there exists an isomorphism ft: t*E → E for each k-rational point t in T, where t: X → X is the action of t. Equivariant vector bundles have T-linearizations (see Definition 1.2 and [2], [4]), hence we consider T-linearized vector bundles.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 111 , September 1988 , pp. 25 - 40
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

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