Automorphism group of Batyrev Calabi-Yau threefolds

TL;DR

This paper proves that all Batyrev Calabi-Yau threefolds derived from certain fourfolds have finite automorphism groups, supporting the conjecture that their Kahler cones are polyhedral and ample.

Contribution

It establishes the finiteness of automorphism groups for a broad class of Batyrev Calabi-Yau threefolds, linking to conjectures about their Kahler cones.

Findings

All Batyrev Calabi-Yau threefolds from small resolutions have finite automorphism groups.

Supports Morrison's conjecture on the polyhedral structure of Kahler cones.

Provides geometric insights into the automorphism groups of Calabi-Yau threefolds.

Abstract

In this paper, we will prove that all Batyrev Calabi-Yau threefolds, arising from a small resolution of a generic hyperplane section of a reflexive Fano-Gorenstein fourfold, have finite automorphism group. Together with Morrison conjecture, this suggests that Batyrev Calabi-Yau threefolds should have a polyhedral Kahler (ample) cone.