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Conjecture
$\mathcal{O}$ holds for some horospherical varieties of
Picard rank 1
Lela Bones, Garrett Fowler, Lisa Schneider and Ryan M. Shifler |
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Vol. 13 (2020), No. 4, 551–558
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Abstract |
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Property for an arbitrary complex, Fano manifold is a statement about the eigenvalues of the linear operator obtained from the quantum multiplication of the anticanonical class of . Conjecture is a conjecture that property holds for any Fano variety. Pasquier classified the smooth nonhomogeneous horospherical varieties of Picard rank 1 into five classes. Conjecture has already been shown to hold for the odd symplectic Grassmannians, which is one of these classes. We will show that conjecture 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. |
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Keywords
quantum cohomology, horospherical, conjecture $\mathcal{O}$
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Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14N15, 15B48
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Milestones
Received: 10 July 2018
Revised: 12 July 2019
Accepted: 25 July 2020
Published: 20 November 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Lela Bones | |
| Department of Mathematics Salisbury University Salisbury, MD United States |
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| Garrett Fowler | |
| Department of Mathematics Salisbury University Salisbury, MD United States |
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| Lisa Schneider | |
| Department of Mathematics Salisbury University Salisbury, MD United States |
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| Ryan M. Shifler | |
| Department of Mathematics Salisbury University Salisbury, MD United States |
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| © 2020 MSP (Mathematical Sciences Publishers). |
