Abstract
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.
Citation
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
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