Automorphisms of Calabi-Yau threefolds from algebraic dynamics and the second Chern class

TL;DR

This paper explores automorphisms of strict Calabi-Yau threefolds, discussing speculative ideas related to algebraic dynamics and the second Chern class, inspired by recent questions in the field.

Contribution

It presents new conjectural perspectives on the automorphisms of Calabi-Yau threefolds, connecting algebraic dynamics with geometric invariants.

Findings

Proposes conjectures linking automorphisms to the second Chern class

Suggests new directions for understanding symmetries of Calabi-Yau threefolds

Highlights open problems in the automorphism groups of Calabi-Yau varieties

Abstract

This is a report of my talk at MFO after Cetraro this July consisting of more speculations, rather than definite results, on automorphisms of strict Calabi-Yau threefolds in the view of the question posed in my ICM report after Dinh, Sibony and D.-Q. Zhang.