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

Abstract

In this article, we examine the arithmetic aspect of the Kummer-surface-type CY 3-folds $\widehat{T/G}$, characterized by the crepant resolution of 3-torus-orbifold $T/G$ with only isolated singularities. Up to isomorphisms, there are only two such space $\widehat{T/G}$ 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 $\widehat{T/G}$ are identified explicitly as the corresponding elliptic curve appeared in the structure of $T$. We further provide the $\QZ$-structure of $\widehat{T/G}$ and verify their modularity property.

Latex 13 pages; Typos corrected, New improved and extended version with rational structures of CY spaces completed and their modular property verified

References in corpus (1)

• Rational Curves in Rigid Calabi-Yau Three-folds