Hilbert coefficients of Schubert varieties in Grassmannians

Abstract

In this paper, we give combinatorial formulas for the Hilbert coefficients, h-polynomial and the Cohen–Macaulay type of Schubert varieties in Grassmannians in terms of the posets associated with them. As a consequence, necessary conditions for a Schubert variety to be a complete intersection and combinatorial criteria are given for a Schubert variety to be Gorenstein and almost Gorenstein, respectively.