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

Abstract

AbstractWe 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.