Calabi-Yau Three-folds of Type K (I): Classification

Any Calabi-Yau three-fold X with infinite fundamental group admits an étale Galois covering either by an abelian three-fold or by the product of a K3 surface and an elliptic curve.Wecall X of type A in the former case and of type K in the latter case. In this article, we provide the full classification of Calabi-Yau three-folds of type K, based on Oguiso and Sakurai's work [25]. Together with a refinement of their result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau three-folds with infinite fundamental group.