论文标题
猜想$ \ MATHCAL {O} $适用于Picard Rank 1
Conjecture $\mathcal{O}$ holds for some Horospherical Varieties of Picard Rank 1
论文作者
论文摘要
属性$ \ MATHCAL {O} $对于任意复合物，Fano歧管$ x $，是关于从$ x $的抗宗教类别的量子乘法获得的线性操作员的特征值的声明。猜想$ \ MATHCAL {O} $是一个猜想，属性$ \ MATHCAL {O} $对于任何Fano品种都包含。 Pasquier列出了Picard Rank 1的平滑非殖民霍斯氏品种，分为五个类别。猜想$ \ MATHCAL {O} $已经被证明是为了奇怪的司法草个子，这是其中之一。我们将证明，猜想$ \ Mathcal {O} $在第三类Pasquier列表中保留了两个类别和一个示例。 Perron-Frobenius的理论将我们的证据减少为图理论。
Property $\mathcal{O}$ 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 $\mathcal{O}$ is a conjecture that Property $\mathcal{O}$ holds for any Fano variety. Pasquier listed the smooth non-homogeneous horospherical varieties of Picard rank 1 into five classes. Conjecture $\mathcal{O}$ has already been shown to hold for the odd symplectic Grassmannians which is one of these classes. We will show that Conjecture $\mathcal{O}$ 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.
