发表机构
Kyoto University; Fukuoka University（京都大学; 福冈大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明光滑射影环簇切丛含正秩丰富局部自由子层时同构于射影空间，还建立了Beauville上同调刻画的环簇形式，且指出无环簇假设时相关刻画在特征2下不成立。
AI 中文摘要
我们证明，在任意特征的代数闭域上，若光滑射影环簇的切丛包含正秩的丰富局部自由子层，则该环簇同构于射影空间，且不要求该子层具有环面等变结构。证明用到本原关系、环簇欧拉序列与无特征上同调提升。作为同一方法的应用，我们建立了Beauville的射影空间与二次型的上同调刻画的环簇形式，包括极化。若无环簇假设，这两种刻画在特征2下不成立。
英文摘要
We prove that a smooth projective toric variety over an algebraically closed field of arbitrary characteristic is isomorphic to a projective space if its tangent bundle contains an ample locally free subsheaf of positive rank. No torus-equivariant structure on this subsheaf is assumed. The proof uses primitive relations, the toric Euler sequence, and characteristic-free cohomological lifting. As an application of the same method, we establish the toric form of Beauville's cohomological characterization of projective spaces and quadrics, including the polarization. Without the toric hypothesis, both characterizations fail in characteristic two.
Comments13 pages. Theorem 1.1 now also classifies the ample locally free subsheaf
