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

TL;DR

This paper completes the classification of Calabi-Yau threefolds with infinite fundamental group, focusing on those of type K, which are covered by a product of a K3 surface and an elliptic curve.

Contribution

It provides a full classification of Calabi-Yau threefolds of type K, building on prior work and refining classifications for type A, thereby completing the classification of all such threefolds with infinite fundamental group.

Findings

Complete classification of Calabi-Yau threefolds of type K

Refinement of classification for Calabi-Yau threefolds of type A

Unified classification of Calabi-Yau threefolds with infinite fundamental group

Abstract

Any Calabi-Yau threefold X with infinite fundamental group admits an \'etale 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.