论文标题
对角的短分辨率，用于光滑的Picard Rank 2
A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
论文作者
论文摘要
给定平滑的投射折叠品种$ x $ PICARD等级2，我们通过长度$ \ dim {x} $的线性复合体在$ x \ times x $上解决对角线，由有限直接直接捆绑包组成。作为应用，我们证明了贝克斯施夫 - 史密斯的猜想的新案例，该案例预测了希尔伯特的虚拟分辨率的Syzygy定理的一个版本，并且我们获得了shorrocks-type的矢量拆分标准，用于Picard Cark 2的光滑投影型杂种，扩展了Eisenbud-schre的结果。在PICARD等级2的平滑投射曲折品种的情况下，我们还将其结果提供新的证据，这是Orlov的猜想，内容涉及派生类别的rouquier维度。
Given a smooth projective toric variety $X$ of Picard rank 2, we resolve the diagonal sheaf on $X \times X$ by a linear complex of length $\dim{X}$ consisting of finite direct sums of line bundles. As applications, we prove a new case of a conjecture of Berkesch-Erman-Smith that predicts a version of Hilbert's Syzygy Theorem for virtual resolutions, and we obtain a Horrocks-type splitting criterion for vector bundles over smooth projective toric varieties of Picard rank 2, extending a result of Eisenbud-Erman-Schreyer. We also apply our results to give a new proof, in the case of smooth projective toric varieties of Picard rank 2, of a conjecture of Orlov concerning the Rouquier dimension of derived categories.
