Todd classes of affine cones of Grassmannians

Abstract

A local ring R is said to be a Roberts ring if tau_R([R]) = [Spec R]_dim R, where tau_R is the Riemann-Roch map for Spec R. Such rings satisfy a vanishing theorem for the Serre intersection multiplicity, as was established by Paul Roberts in his proof of the Serre vanishing conjecture. It is known that complete intersections are Roberts rings, and the first author proved that a determinantal ring is a Roberts ring precisely if it is complete intersection. Let A_d(n) denote the affine cone of the Grassmannian G_d(n) under the Plucker embedding. We determine which of the rings A_d(n) are Roberts rings.