[HTML][HTML] An effective decomposition theorem for Schubert varieties

F Cioffi, D Franco, C Sessa - Journal of Symbolic Computation, 2024 - Elsevier
Given a Schubert variety S contained in a Grassmannian G k (C l), we show how to obtain
further information on the direct summands of the derived pushforward R π⁎ QS˜ given by …

A footnote to a paper of Deodhar

D Franco - arXiv preprint arXiv:2308.01585, 2023 - arxiv.org
Let $ X\subseteq G\slash B $ be a Schubert variety in a flag manifold and let $\pi:\tilde
X\rightarrow X $ be a Bott-Samelson resolution of $ X $. In this paper we prove an effective …

On the Computation of the Cohomological Invariants of Bott–Samelson Resolutions of Schubert Varieties

D Franco - Bulletin of the Iranian Mathematical Society, 2024 - Springer
Abstract Let\(X\subseteq G/\mathcal {B}\) be a Schubert variety in a flag manifold and
let\(\pi:\tilde {X}\rightarrow X\) be a Bott–Samelson resolution of X. In this paper, we prove an …

Polynomial identities related to special Schubert varieties

F Cioffi, D Franco, C Sessa - Applicable Algebra in Engineering …, 2023 - Springer
Let\mathcal SS be a single condition Schubert variety with an arbitrary number of strata.
Recently, an explicit description of the summands involved in the decomposition theorem …

Intersection Cohomology and Severi Varieties

V Di Gennaro, D Franco - The Art of Doing Algebraic Geometry, 2023 - Springer
Let be a smooth projective variety. Consider the intersection cohomology complex of the
local system, where denotes the projection from the universal hyperplane family of to. We …

[PDF][PDF] Poincare Polynomial Identities for Special Schubert Varieties

F Cioffi, D Franco, C Sessa - puremath.no
(⋆): Z⊆ V and dim (V∩ F)= iq. Let i:∆ 0 q↩→∆ p be inclusion, let πp:∆ p→∆ p and ρpq:∆ 0
pq→∆ 0 q be projection onto the first and second factor, respectively. ρpq is a fibration with …