Curve neighborhoods of Seidel products in quantum cohomology
Mihail \c{T}arigradschi
TL;DR
This paper proves a conjecture relating curve neighborhoods and Schubert varieties in quantum cohomology for type A flag varieties, clarifying the geometric structure of Seidel products.
Contribution
It confirms the Buch-Chaput-Perrin conjecture for type A flag varieties, establishing a precise geometric description of Seidel product neighborhoods.
Findings
Curve neighborhoods of Seidel products are Schubert varieties in type A.
The conjecture holds specifically for flag varieties of type A.
Provides a geometric interpretation of quantum Seidel products.
Abstract
A conjecture of Buch-Chaput-Perrin asserts that the two-pointed curve neighborhood corresponding to a quantum product of Seidel type is an explicitly given Schubert variety. We prove this conjecture for flag varieties in type A.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic Geometry and Number Theory · Alkaloids: synthesis and pharmacology