On Kummer 3-folds

某些 Kummer Calabi-Yau 3-重簇的 Zeta 函数

Zeta function of some Kummer Calabi-Yau 3-folds

本文计算了特定文献中引入并研究的 Kummer Calabi-Yau 3-重簇的 Hodge 数和 zeta 函数。

Nef Cone of a Generalized Kummer 4-fold

In this note, we calculate the boundary of movable cones and nef cones of the generalized Kummer 4-fold $\mathrm{Km}^2(A)$ attached to an abelian surface $A$ with $\mathrm{rkNS}(A) = 1$.

Fiber products of elliptic surfaces with section and associated Kummer fibrations

We investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find formulas to compute the Hodge numbers of obtained three folds in terms of the types of singular fibers of the elliptic surfaces. Next we study Kummer fibrations associated to these fiber products.

Intermediate Jacobian and Some Arithmetic Properties of Kummer-surface-type CY 3-folds

In this article, we examine the arithmetic aspect of the Kummer-surface-type CY 3-folds $\hat{T/G}$, characterized by the crepant resolution of 3-torus-orbifold $T/G$ with only isolated singularities. Up to isomorphisms, there are only two such space $\hat{T/G}$ with $|G|=3, 7$, and both $T$ carrying the structure of triple-product structure of a CM elliptic curve. The (Griffiths) intermediate Jacobians of these $\hat{T/G}$ are identified explicitly as the corresponding elliptic curve appeared in the structure of $T$. We further provide the $\QZ$-structure of $\hat{T/G}$ and verify their modul…