Toric ideals of root systems

Hidefumi Ohsugi

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


Abstract

Toric ideals associated with root systems are studied. First, we show the existence of squarefree quadratic initial ideals for configurations arising from the set of positive roots of root systems together with the origin. In particular, corresponding affine semigroup rings are Koszul. Second, we discuss squarefree initial ideals and unimodular coverings for configurations arising from the set of positive roots of root systems together with the origin, without the origin, and thier subconfigurations. It is well-known that corresponding affine semigroup ring is normal if the toric ideal has a squarefree initial ideal or if the convex hull of the configuration has a unimodular covering.


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