论文标题
全面的抗议日志del pezzo表面的特殊收藏
Full exceptional collections for anticanonical log del Pezzo surfaces
论文作者
论文摘要
本文由同源镜子对称性的激励，构建了与约翰逊和科拉尔构建的一系列log del pezzo表面相关的规范堆栈明确的特殊集合。这些表面具有环状商，非戈伦斯坦，奇异性。该结构涉及$ \ mathrm {gl}（2，\ mathbb {c}）$ mckay对应关系，以及对表面最小分辨率的研究，这些分辨率是两个del pezzo表面的依据。我们表明，当且仅当它接受广义的Eckardt点时，就以这种方式出现了两个Del Pezzo表面，并且在论文的过程中，我们将$ \ Mathbb {p}^2 $的爆炸归类为产生它们。我们对Ishii-ueda函数的伴随的结果适用于$ \ Mathrm {gl}（2，\ Mathbb {c}）$的任何有限的小子组。
Motivated by homological mirror symmetry, this paper constructs explicit full exceptional collections for the canonical stacks associated with the series of log del Pezzo surfaces constructed by Johnson and Kollár. These surfaces have cyclic quotient, non-Gorenstein, singularities. The construction involves both the $\mathrm{GL}(2,\mathbb{C})$ McKay correspondence, and the study of the minimal resolutions of the surfaces, which are birational to degree two del Pezzo surfaces. We show that a degree two del Pezzo surface arises in this way if and only if it admits a generalized Eckardt point, and in the course of the paper we classify the blow-ups of $\mathbb{P}^2$ giving rise to them. Our result on the adjoints of the functor of Ishii-Ueda applies to any finite small subgroup of $\mathrm{GL}(2,\mathbb{C})$.
