On Canonical Modules of Toric Face Rings
نویسنده
چکیده
Generalizing the concepts of Stanley–Reisner and affine monoid algebras, one can associate to a rational pointed fan Σ in Rd the Zd-graded toric face ring K[Σ]. Assuming that K[Σ] is Cohen–Macaulay, the main result of this paper is to characterize the situation when its canonical module is isomorphic to a Zd-graded ideal of K[Σ]. From this result several algebraic and combinatorial consequences are deduced in the situations where Σ may be related to a manifold with non-empty boundary, or Σ is a shellable fan.
منابع مشابه
On Toric Face Rings
Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley–Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley–Reisnerand affine monoid algebras. We consider (nonpure) shellable fan’s and the Cohen–Macaulay property. More...
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