Commutative Algebra and Algebraic Geometry: Isotonian Algebras

Seminar | February 14 | 3:45-4:45 p.m. | 939 Evans Hall

 Mina Bigdeli, MSRI

 Department of Mathematics

To a pair P and Q of finite posets we attach the toric ring K[P, Q] whose generators are in bijection to the isotone maps from P to Q. This class of algebras, called isotonian, are natural generalizations of the so-called Hibi rings.

In this talk we introduce isotonian algebras and then state their Krull dimension. We discuss particular classes of posets P and Q for which the toric ring K[P, Q] is normal, and the classes that the defining ideal of their isotonian algebras admits a quadratic Gröbner basis. This talk is based on a joint work with J. Herzog, T. Hibi, A. Qureshi and A. Shikama.