以阿斯平沃尔和莫里森为例

Aspinwall-Morrison计算和Gromov-Witten理论

The Aspinwall-Morrison calculation and Gromov-Witten theory

通过将Aspinwall-Morrison公式的计算与Gromov-Witten理论相联系，证明了Aspinwall-Morrison公式。

关于Aspinwall、Morrison和Szendrői的一个例子

On an example of Aspinwall, Morrison, and Szendrői

本文研究Aspinwall和Morrison引入的Calabi-Yau 3-折叠1参数族Y_t，通过证明其不同成员的整Hodge结构不同，证实了Szendrői关于它们不双有理且不导出等价的猜想，并讨论了其与Torelli型定理及反例的关系。

广义Calabi-Yau结构、K3曲面和B-域

Generalized Calabi-Yau structures, K3 surfaces, and B-fields

在K3曲面的情形下研究了Hitchin最近提出的广义Calabi-Yau结构。我们展示了它们是如何与经典理论的K3曲面和模空间的某些SCFT研究Aspinwall和莫里森。事实证明，K3曲面和辛结构都是这个一般概念的特殊情况。广义Calabi-Yau结构的模空间存在一个标准辛形式，关于该标准辛形式，辛结构的模空间是拉格朗日的。K3曲面的标准理论包含周期映射的满射性和整体Torelli定理的弱形式。

Generalized Shioda--Inose structures of order 3

A Shioda--Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison's results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore we define the generalized Shioda--Inose structur…

The length classification of threefold flops via noncommutative algebras

Smooth threefold flops with irreducible centres are classified by the length invariant, which takes values 1, 2, 3, 4, 5 or 6. This classification by Katz and Morrison identifies 6 possible partial resolutions of Kleinian singularities that can occur as generic hyperplane sections, and the simultaneous resolutions associated to such a partial resolution produce the universal flop of length $l$. In this paper we translate these ideas into noncommutative algebra. We introduce the universal flopping algebra of length $l$ from which the universal flop of length $l$ can be recovered by a moduli con…

关于Calabi-Yau超曲面的Cox环

On Cox Rings of Calabi-Yau hypersurfaces

本文研究了平滑反canonical Calabi-Yau超曲面在平滑的toric Fano变种中的Cox环，通过研究环境Fano多面体的原始对的组合学以及嵌入变种的Cox环描述，确定了几种配置使得超曲面是Mori梦想空间，并获得了其Cox环的显式表示。此外，本文还展示了某些组合配置迫使birational自同构群为无限，从而在三维和四维中揭示了Cox环有限生成与无限birational自同构群之间的二元对立。最后，对于一类非Mori梦想的例子，证明了Morrison-Kawamata锥猜想对于可动锥。