发表机构
The Chinese University of Hong Kong, Shenzhen; Tsinghua University; Sun Yat-sen University（香港中文大学（深圳）; 清华大学; 中山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明度数至多四的 del Pezzo 曲面可由结构层的增强右正交补决定，并通过 Hochschild-Serre 代数、旋量修正等构造与刻画其重构。
AI 中文摘要
我们证明，对于每一个度数至多为四的光滑复 del Pezzo 曲面，结构层的增强右正交补决定了该曲面（在同构意义下）。在度数一、二、三的情形中，我们通过分次矩阵分解，从 Hochschild-Serre 代数的内在部分恢复反典范方程；在度数四的情形中，相关的 Serre 对角恢复与二次曲面束相联系的轨道规范环。我们还利用 Bertini 与 Geiser 对合、等变拓扑 K-理论以及经典 Torelli 定理，在度数一和二的情形给出另一种证明。然后，我们研究射影直线上的圆锥丛结构所关联的 Clifford 分量。在每一个度数至多为四的情形中，我们构造一个抽象旋量丛，其旋量修正产生另一个通常非同构的 del Pezzo 曲面。我们通过 Kuznetsov 修正定理表明，相关的基础线性等价恰好是由旋量修正所诱导的那些。
英文摘要
We prove that, for every smooth complex del Pezzo surface of degree at most four, the enhanced right orthogonal to the structure sheaf determines the surface up to isomorphism. In degrees one, two, and three, we recover the anticanonical equation from intrinsic pieces of the Hochschild-Serre algebra via graded matrix factorizations; in degree four, the relevant Serre diagonal recovers the orbifold canonical ring associated with the pencil of quadrics. We also give an alternative proof in degrees one and two using the Bertini and Geiser involutions, equivariant topological K-theory, and classical Torelli. Then, we study the Clifford component associated with a conic bundle structure over the projective line. In every degree at most four, we construct an abstract spinor bundle whose spinor modification produces another, generally non-isomorphic, del Pezzo surface. We show via Kuznetsov's modification theorem that the relevant base-linear equivalences are precisely those induced by spinor modifications.
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