ON CANONICAL MODULES OF TORIC FACE RINGS

Abstract

Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan Sigma in R-n the Z(d)-graded toric face ring K[Sigma]. Assuming that K[Sigma] is Cohen-Macaulay, the main result of this paper is to characterize the situation when its canonical module is isomorphic to a Z(d)-graded ideal of K[Sigma]. From this, result several algebraic and combinatorial consequences axe deduced. As an application, we give a relation between the cleanness of K[Sigma] and the shellability of Sigma.