Vanishing Results for Toric Varieties Associated to $GL_n$ and $G_2$
Algebraic Geometry
2011-11-09 v2
Abstract
Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles on toric varieties associated to and . This can be considered of general interest and it improves the previously known results for these varieties. We also show how these results give a simple proof of a converse to Mazur's inequality for and respectively. It is known that the latter imply the non-emptiness of some affine Deligne-Lusztig varieties.
Keywords
Cite
@article{arxiv.math/0605701,
title = {Vanishing Results for Toric Varieties Associated to $GL_n$ and $G_2$},
author = {Qëndrim R. Gashi},
journal= {arXiv preprint arXiv:math/0605701},
year = {2011}
}