2020/11/28 by Lela Bones, Bones, Lela, Garrett Fowler +5
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2011.14154
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 listed the smooth non-homogeneous 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. The theory of Perron-Frobenius reduces our proofs to be graph-theoretic in nature.