Binomial ideals attached to finite collections of cells

Abstract

We consider the ideal of inner 2-minors $I_{\mathcal{P}}$ of a finite set of cells $\mathcal{P}$, which we call the cell ideal of $\mathcal{P}$. A nice interpretation for the height of an unmixed ideal $I_{\mathcal{P}}$, in terms of the number of cells of $\mathcal{P}$ is given. Moreover, the coordinate rings of cell ideals with isolated singularities are determined.

Keywords:

• Cell ideal
• height
• isolated singularity

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13F20
• 05E40

Acknowledgement

The second author was partially supported by JSPS KAKENHI 19H00637. The third author is supported by the Alexander von Humboldt Foundation.