Vanishing Results for Toric Varieties Associated To GL n and G2 |
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Authors: | Qëndrim R. Gashi |
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Affiliation: | (1) Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA |
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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 GL n and G2. 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 GL n and G2 respectively. It is known that the latter imply the nonemptiness of some affine Deligne–Lusztig varieties. Dedicated to Scarlett MccGwire and Dr. Christian Duhamel |
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