Positivity determines the quantum cohomology of the odd symplectic Grassmannian of lines
Abstract
Abstract Let IG:=IG(2,2𝑛+1) denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring QH*(IG) has negative structure constants. For 𝑛≥3, we give a positivity condition that implies the quantum cohomology ring QH*(IG) is the only quantum deformation of the cohomology ring H*(IG) up to the scaling of the quantum parameter. This is a modification of a conjecture by Fulton. Keywords: Positivity, quantum deformation, quantum cohomology. 2020 MATHEMATICS SUBJECT CLASSIFICATION: Primary: 14N35, Secondary: 14N15, 14M15. Acknowledgments: I would like to thank an anonymous referee for identifying a gap in the argument for the |λ|>2n case. I would also like to thank Leonardo Mihalcea for a very useful conversation.
Faculty Members
- Ryan M. Shifler - Department of Mathematical Sciences, Henson Science Hall, Salisbury University, Salisbury, Maryland, USA
Themes
- Cohomology rings
- Mathematical modifications of conjectures
- Positivity conditions
- Quantum cohomology
- Quantum deformation