K3 surfaces with non-symplectic automorphisms of order three and Calabi-Yau orbifolds

Abstract

Let S be a K3 surface that admits a non-symplectic automorphism $\rho$ of order 3. We divide $S\times {\mathbb{P}}^1$ by $\rho \times \psi$ where $\psi$ is an automorphism of order 3 of ${\mathbb{P}}^1$. There exists a threefold ramified cover of a partial crepant resolution of the quotient that is a Calabi-Yau orbifold. We compute the Euler characteristic of our examples and obtain values ranging from 30 to 219.

arXiv comment10 pages; v2: Further references and minor corrections are added; v3: We clarified that our examples are in fact orbifolds