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NORMALITY AND QUADRATICITY FOR SPECIAL AMPLE LINE BUNDLES ON TORIC VARIETIES ARISING FROM ROOT SYSTEMS

Published online by Cambridge University Press:  01 October 2013

QËNDRIM R. GASHI  and
TRAVIS SCHEDLER
QËNDRIM R. GASHI
Affiliation:
Department of Mathematics, University of Prishtina, Pristina 10000, Kosovo e-mail: qendrim@gmail.com
TRAVIS SCHEDLER
Affiliation:
Department of Mathematics, The University of Texas at Austin 2515 Speedway, Austin, TX 78712-1202, USA e-mail: trasched@gmail.com
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Abstract

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We prove that special ample line bundles on toric varieties arising from root systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl chambers, and special means that the bundle is torus-equivariant such that the character of the line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that chamber. Moreover, we prove that the associated semi-group rings are quadratic.

Keywords

17B2214M25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue A: New developments in Noncommutative Algebra and its applications. A conference in honour of Kenny Brown's and Toby Stafford's 60th birthdays. , October 2013 , pp. 113 - 134
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

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