Calabi-Yau threefolds of type K (I): Classification

Kenji Hashimoto, Atsushi Kanazawa

Published 2014-09-26Version 1

Any Calabi-Yau threefold X with infinite fundamental group admits an \'{e}tale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the latter case. In this paper, we provide the full classification of Calabi-Yau threefolds of type K, based on Oguiso and Sakurai's work. Together with a refinement of Oguiso and Sakurai's result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau threefolds with infinite fundamental group.