Geometric Invariant Theory for principal three-dimensional subgroups acting on flag varieties

Autor:	Seppänen, Henrik, Tsanov, Valdemar V.
Rok vydání:	2015
Předmět:	Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	Let G be a semisimple complex Lie group. In this article, we study Geometric Invariant Theory on a flag variety G/B with respect to the action of a principal 3-dimensional simple subgroup S of G. We determine explicitly the GIT-equivalence classes of S-ample line bundles on G/B. We show that, under mild assumptions, among the GIT-classes there are chambers, in the sense of Dolgachev-Hu. The Hilbert quotients Y=X//S with respect to various chambers form a family of Mori dream spaces, canonically associated with G. We are able to determine three important cones in the Picard group of any of these quotients: the pseudo-effective, the movable and the nef cones. Comment: 20 pages, substantially improved exposition with more detailed results
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1503.07105 Zobrazit plný text záznamu View this record from Arxiv