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A vanishing result for toric varieties associated with root systems. (English) Zbl 1133.14054
The author proves the vanishing of the higher cohomology groups for certain line bundles on the toric variety corresponding to a root system. These results are related to a converse to Mazur’s inequality for simply connected split reductive algebraic groups.

##### MSC:
 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 14F17 Vanishing theorems in algebraic geometry 14F30 $$p$$-adic cohomology, crystalline cohomology
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