Grobner Bases and Linear Strands of Determinantal Facet Ideals

Abstract: Determinantal facet ideals (DFI's) are a generalization of binomial edge ideals which were introduced by Ene, Herzog, Hibi, and Mohammedi. The generating sets for such ideals come from matrix minors whose columns are parametrized by an associated simplicial complex. In this talk, we will discuss a generalized version of DFI's and give explicit conditions guaranteeing that the standard minimal generating set forms a reduced Grobner basis (with respect to the standard diagonal term order). Moreover, we show that the linear strand of the initial ideal may be obtained as a "sparse" generalized Eagon-Northcott complex, which may then be used to verify a conjecture relating the graded Betti numbers of a DFI to the graded Betti numbers of its initial ideal. This is joint work with Ayah Almousa.

commutative algebraalgebraic geometrycombinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

Geometry, Algebra, Singularities, and Combinatorics

Series comments: Please contact Peter Crooks to be placed on the mailing list.