Rigidity of equivariant Schubert classes

Abstract

We prove that Schubert varieties in flag manifolds are uniquely determined by their equivariant cohomology classes, as well as a stronger result that replaces Schubert varieties with closures of Bialynicki-Birula cells under suitable conditions. This is used to prove that any two-pointed curve neighborhood representing a quantum cohomology product with a Seidel class is a Schubert variety.