The Aspinwall-Morrison calculation and Gromov-Witten theory

On an example of Aspinwall and Morrison

In this paper, a family of smooth multiply connected Calabi--Yau threefolds is investigated. The family presents a counterexample to global Torelli as conjectured by Aspinwall and Morrison.

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。

Multiple Cover Calculation for the Unramified Compactification of the Moduli Space of Stable Maps

In this paper we compute the multiple cover Gromov-Witten integrals (analog of the Aspinwall-Morrison formula) for the unramified compactification of the moduli space of stable maps to an embedded $\PO$ in a Calabi-Yau threefold $X$ with the normal bundle $\mathcal{O}_{\PO}(-1) \bigoplus \mathcal{O}_{\PO}(-1)$.

On the quantum cohomology of a symmetric product of an algebraic curve

The dth symmetric product of a curve of genus g is a smooth projective variety. This paper is concerned with the little quantum cohomology ring of this variety, that is, the ring having its 3-point Gromov-Witten invariants as structure constants. This is of considerable interest, for example as the base ring of the quantum category in Seiberg-Witten theory. The main results give an explicit, general formula for the quantum product in this ring unless d is in the narrow interval [3/4 g, g-1). Otherwise, they still give a formula modulo third order terms. Explicit generators and relations are al…

镜像五次方程中线的开放枚举镜像对称

Open enumerative mirror symmetry for lines in the mirror quintic

本文假设负循环开闭映射存在，从同调镜像对称推导出五次三维流形某些拉格朗日子流形的开放Gromov-Witten不变量的镜像定理，其OGW不变量与Walcher的相对周期积分一致，且涉及Dirichlet L函数特殊值，还解释了相关双曲拉格朗日存在性预测。