Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus

Yi Hu

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Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus

Yi Hu

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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.

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BibTeX RIS

Yi Hu. 2006-05-01. Quotients by Reductive Group, Borel Subgroup, Unipotent Group and Maximal Torus. https://arxiv.org/abs/math/0605008

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