W-translated Schubert divisors and transversal intersections

TL;DR

This paper investigates the toric degeneration of translated Schubert divisors in type A flag varieties using Gelfand-Cetlin polytopes, proposing and verifying a conjecture about their transversal intersections.

Contribution

It introduces a conjecture on transversal intersections of Schubert varieties and verifies it in specific cases like Grassmannians and complete flag varieties.

Findings

Verified the conjecture for Gr(2, n)

Confirmed the conjecture for Fl_4

Connected toric degenerations with intersection properties

Abstract

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety of Lie type A via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including complex Grassmannian Gr(2, n) and complete flag variety Fl_4.