Hilbert functions of ladder determinantal varieties

We outline the computation of an explicit formula for the Hilbert function of the ladder determinantal varieties defined by the vanishing of all minors of a fixed size of a rectangular matrix with indeterminate entries such that the indeterminates in these minors are restricted to lie in some ladder shaped region of the rectangular array. Finding such a formula is equivalent to enumerating the set of monomials of a fixed degree such that the support of these monomials is a subset of a `ladder' and satisfies a certain "index condition". We also describe applications of this formula for estimating the dimension of ladder determinantal varieties.

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Sudhir R. Ghorpade
• Keywords: DM 2002, Explicit Formula, Ladder Determinantal Varieties, Ladder Shaped Region