Hilbert functions of ladder determinantal varieties (Q1348145)

In the paper under review the author studies algebraic varieties defined by minors of a fixed size of a matrix such that all minors are restricted to lie in a ladder shaped region. The main result are explicit formulas for the Hilbert functions and Hilbert series related to these varieties. In particular, the author shows that, although the formulas in the general case are complicated, they can be used to derive fairly simple estimates for some useful geometric invariants of the varieties such as the degree of the Hilbert polynomial.