Polynomial identities related to special Schubert varieties

Author:

Cioffi Francesca,Franco Davide,Sessa Carmine

Abstract

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

Funder

Università degli Studi di Napoli Federico II

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory

Reference24 articles.

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1. An effective decomposition theorem for Schubert varieties;Journal of Symbolic Computation;2024-03

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