Non-normal affine monoids

Abstract

We give a geometric description of the set of holes in a non-normal affine monoid $Q$. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of $k[Q]$. From this, we see how various properties of $k[Q]$ like local normality and Serre's conditions $(R_1)$ and $(S_2)$ are encoded in the geometry of the holes. A combinatorial upper bound for the depth the monoid algebra $k[Q]$ is obtained and some cases where equality holds are identified. We apply this results to seminormal affine monoids.

18 pages, 3 figures. Simplified proof of the main result, shortened. An even shorter version appeared with the title "Non-normal affine monoid algebra" in manuscripta mathematica

References in corpus (2)

• Lectures on 0/1-polytopes
• On seminormal monoid rings