J. Korean Math. Soc. 2002; 39(3): 331-349
Printed May 1, 2002
Copyright © The Korean Mathematical Society.
Mikiya Masuda
Osaka City University
Let $G$ be a reductive algebraic group and let $B, F$ be $G$-modules. We denote by $\text{VEC}_G(B,F)$ the set of isomorphism classes in algebraic $G$-vector bundles over $B$ with $F$ as the fiber over the origin of $B$. Schwarz (or Kraft-Schwarz) shows that $\text{VEC}_G(B,F)$ admits an abelian group structure when $\dim B/\!\!/G=1$. In this paper, we introduce a stable functor $\text{VEC}_G(B,F^\infty)$ and prove that it is an abelian group for any $G$-module $B$. We also show that this stable functor will have nice properties.
Keywords: vector bundle, reductive algebraic group, moduli, invariant theory
MSC numbers: Primary 14D20; Secondary 14R20
2007; 44(6): 1339-1350
2010; 47(2): 299-309
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