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VOL. 33 | 2002 Certain Moduli of Algebraic $G$-vector Bundles over Affine $G$-varieties

Abstract

Let $G$ be a reductive complex algebraic group and $P$ a complex $G$-module with algebraic quotient of dimension $\ge 1$. We construct a map from a certain moduli space of algebraic $G$-vector bundles over $P$ to a $\mathbb{C}$-module possibly of infinite dimension, which is an isomorphism under some conditions. We also show non-triviality of moduli of algebraic $G$-vector bundles over a $G$-stable affine hypersurface of some type. In particular, we show that the moduli space of algebraic $G$-vector bundles over a $G$-stable affine quadric with fixpoints and one-dimensional quotient contains $\mathbb{C}^p$.

Information

Published: 1 January 2002
First available in Project Euclid: 31 December 2018

zbMATH: 1076.14543
MathSciNet: MR1890099

Digital Object Identifier: 10.2969/aspm/03310165

Subjects:
Primary: 14D20, 14R20

Rights: Copyright © 2002 Mathematical Society of Japan

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