Non-liftable Calabi-Yau spaces

TL;DR

This paper constructs numerous new three-dimensional Calabi-Yau spaces in positive characteristic that cannot be lifted to characteristic zero, using a technique involving lifting nodal models to smooth rigid Calabi-Yau spaces.

Contribution

It introduces a novel method for constructing non-liftable Calabi-Yau spaces in positive characteristic through lifting nodal models.

Findings

Many new non-liftable Calabi-Yau threefolds constructed

Technique relies on lifting nodal models to smooth rigid spaces

Advances understanding of Calabi-Yau spaces in positive characteristic

Abstract

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.