An Example of non-simply connected non-liftable Calabi-Yau 3-fold in positive characteristic

TL;DR

This paper presents a specific example of a Calabi-Yau threefold in characteristic 3 that is non-simply connected and cannot be lifted to characteristic zero, expanding understanding of Calabi-Yau varieties in positive characteristic.

Contribution

The paper constructs a non-simply connected, non-liftable Calabi-Yau threefold in characteristic 3, derived from a known simply connected example, demonstrating new phenomena in algebraic geometry.

Findings

Existence of non-simply connected non-liftable Calabi-Yau 3-folds in characteristic 3

Construction method from a simply connected example by Schr"oer

Insight into the structure of Calabi-Yau varieties in positive characteristic

Abstract

We show an example of non-simply connected non-liftable Calabi-Yau threefold over an algebraically closed field of characteristic $3$. It is constructed from a simply connected example by S.~Schr\"oer.