An effective decomposition theorem for Schubert varieties

Given a Schubert variety Scontained in a Grassmannian G(k)(C-l), we show how to obtain further information on the direct summands of the derived pushforward R pi(*)Q (S) over bar Sgiven by the application of the decomposition theorem to a suitable resolution of singularities pi: (S) over bar -> S. As a by-product, Poincar'e polynomial expressions are obtained along with an algorithm which computes the unknown terms in such expressions and which shows that the actual number of direct summands happens to be less than the number of supports of the decomposition. (c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

This article demonstrates how to obtain further information on the direct summands of the derived pushforward by applying the decomposition theorem to a suitable resolution of singularities. It also includes Poincaré polynomial expressions and an algorithm for computing the unknown terms in these expressions.