Quantum cohomology determined with negative structure constants present

Author:

Ryan M. Shifler

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Quantum Algebra (math.QA)

journal:

date:

2023-07-04 16:00:00

Abstract

Let $\mbox{IG}:=\mbox{IG}(2,2n+1)$ denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring $\mbox{QH}^*(\mbox{IG})$ has negative structure constants. For $n \geq 3$, we give a positivity condition that implies the quantum cohomology ring $\mbox{QH}^*(\mbox{IG})$ is the only quantum deformation of the cohomology ring $\mbox{H}^*(\mbox{IG})$ up to the scaling of the quantum parameter. This is a modification of a conjecture by Fulton.

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