Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus
Abstract
Consider an algebraic action of a connected complex reductive algebraic group on a complex polarized projective variety. In this paper, we first introduce the nilpotent quotient, the quotient of the polarized projective variety by a maximal unipotent subgroup. Then, we introduce and investigate three induced actions: one by the reductive group, one by a Borel subgroup, and one by a maximal torus, respectively. Our main result is that there are natural correspondences among quotients of these three actions. In the end, we mention a possible application to the moduli spaces of parabolic bundles over algebraic curves for further research.
Cite
@article{arxiv.math/0605008,
title = {Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus},
author = {Yi Hu},
journal= {arXiv preprint arXiv:math/0605008},
year = {2007}
}
Comments
Dedicated to Robert MacPherson on the occasion of his 60th birthday. MacPherson's special issue, Pure and Applied Mathematics Quarterly (to appear)