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2020 Conjecture $\mathcal{O}$ holds for some horospherical varieties of Picard rank 1
Lela Bones, Garrett Fowler, Lisa Schneider, Ryan M. Shifler
Involve 13(4): 551-558 (2020). DOI: 10.2140/involve.2020.13.551

Abstract

Property 𝒪 for an arbitrary complex, Fano manifold X is a statement about the eigenvalues of the linear operator obtained from the quantum multiplication of the anticanonical class of X. Conjecture 𝒪 is a conjecture that property 𝒪 holds for any Fano variety. Pasquier classified the smooth nonhomogeneous horospherical varieties of Picard rank 1 into five classes. Conjecture 𝒪 has already been shown to hold for the odd symplectic Grassmannians, which is one of these classes. We will show that conjecture 𝒪 holds for two more classes and an example in a third class of Pasquier’s list. Perron–Frobenius theory reduces our proofs to be graph-theoretic in nature.

Citation

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Lela Bones. Garrett Fowler. Lisa Schneider. Ryan M. Shifler. "Conjecture $\mathcal{O}$ holds for some horospherical varieties of Picard rank 1." Involve 13 (4) 551 - 558, 2020. https://doi.org/10.2140/involve.2020.13.551

Information

Received: 10 July 2018; Revised: 12 July 2019; Accepted: 25 July 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190423
Digital Object Identifier: 10.2140/involve.2020.13.551

Subjects:
Primary: 14N35
Secondary: 14N15, 15B48

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2020
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