\'Etale triviality of finite equivariant vector bundles
Algebraic Geometry
2024-12-11 v2 Category Theory
Abstract
Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle E over X is -finite, meaning f_1(E)= f_2(E) as H-equivariant bundles for two distinct polynomials f_1 and f_2 whose coefficients are nonnegative integers, if and only if the pullback of E along some H-equivariant finite \'etale covering of X is trivial as an H-equivariant bundle.
Keywords
Cite
@article{arxiv.2103.06491,
title = {\'Etale triviality of finite equivariant vector bundles},
author = {Indranil Biswas and Peter O'Sullivan},
journal= {arXiv preprint arXiv:2103.06491},
year = {2024}
}