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arXiv · 0710.5751

A Vanishing Result for Toric Varieties Associated with Root Systems

Qëndrim R. Gashi
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Abstract

Consider a root system $R$ and the corresponding toric variety $V_R$ whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for $R$. We prove the vanishing of the higher cohomology groups for certain line bundles on $V_R$ by proving a purely combinatorial result for root systems. These results are related to a converse to Mazur's Inequality for (simply-connected) split reductive groups.

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Qëndrim R. Gashi. 2007-10-30. A Vanishing Result for Toric Varieties Associated with Root Systems. https://arxiv.org/abs/0710.5751

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