Dominik Burek

Title: Higher dimensional Calabi-Yau manifolds of Kummer type

Abstract:
We construct Calabi-Yau manifolds of arbitrary dimensions as a
resolution of a quotient of a product of a K3 surface and (n-2)
elliptic curves with a strictly non-symplectic automorpism of order 2,
3, 4 or 6. This construction generalize a result of Cynk and Hulek and
the classical construction of Borcea and Voisin, the proof is based on
toric resolution of singularities.
Using Chen-Ruan orbifold cohomology we compute the Hodge numbers of
all constructed examples and give a method to compute the local Zeta
functions.
As an application we generalize the construction of Zariski K3
surfaces due to Katsura and Schuett to obtain arbitrarily dimensional
Calabi-Yau manifolds which are Zariski in any characteristic not
congruent to 1 modulo 12.