Given a Schubert variety Scontained in a Grassmannian Gk(Cl), we show how to obtain further information on the direct sum-mands of the derived pushforward Rπ∗Q˜S given by the application of the decomposition theorem to a suitable resolution of singularities π:˜S→S. As a by-product, Poincaré polynomial ex-pressions 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.
An effective decomposition theorem for Schubert varieties / Cioffi, Francesca; Franco, Davide; Sessa, Carmine. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 121:(2024), p. 102238. [10.1016/j.jsc.2023.102238]
An effective decomposition theorem for Schubert varieties
Cioffi Francesca;Franco Davide;Sessa Carmine
2024
Abstract
Given a Schubert variety Scontained in a Grassmannian Gk(Cl), we show how to obtain further information on the direct sum-mands of the derived pushforward Rπ∗Q˜S given by the application of the decomposition theorem to a suitable resolution of singularities π:˜S→S. As a by-product, Poincaré polynomial ex-pressions 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.