Calabi-Yau threefolds with non-Gorenstein involutions

TL;DR

This paper studies Calabi-Yau threefolds with non-Gorenstein involutions, providing elementary facts and classifying those with Picard rank one and non-zero-dimensional fixed loci, extending concepts from K3 surfaces.

Contribution

It introduces a classification of certain Calabi-Yau threefolds with non-Gorenstein involutions, expanding understanding of their fixed loci and involution properties.

Findings

Classified Calabi-Yau threefolds of Picard rank one with non-Gorenstein involutions.

Identified conditions for fixed loci to be non-zero-dimensional.

Extended the analogy of non-symplectic involutions from K3 surfaces to threefolds.

Abstract

The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a higher dimensional generalization of non-symplectic involutions on $K3$ surfaces. We present some elementary facts about Calabi-Yau threefolds with non-Gorenstein involutions. We give a classification of the Calabi-Yau threefolds of Picard rank one with non-Gorenstein involutions whose fixed locus is not zero-dimensional.