Posets of h-vectors of standard determinantal schemes

Abstract

We study the combinatorial structure of the poset H consisting of h-vectors of length s of codimension c standard determinantal schemes, defined by the maximal minors of a t × (t + c − 1) homogeneous, polynomial matrix. We show that H obtains a natural stratification, where each strata contains a maximum h-vector. Moreover, we prove that any h-vector in H is bounded from above by a h-vector of the same length and which corresponds to a codimension c level standard determinantal scheme. Furthermore, we show that the only strata in which there exists also a minimum h-vector is the one consisting of h-vectors of level standard determinantal schemes.

Keywords

• Standard determinantal scheme
• h-vector
• stratification