A remark on the Torelli theorem for cubic fourfolds

TL;DR

This paper provides a concise proof of the Torelli theorem for cubic fourfolds by leveraging the global Torelli theorem for irreducible holomorphic symplectic varieties, simplifying previous approaches.

Contribution

It offers a new, streamlined proof of the Torelli theorem for cubic fourfolds using existing results on holomorphic symplectic varieties.

Findings

Short proof of Torelli theorem for cubic fourfolds

Utilizes Verbitsky's global Torelli theorem for symplectic varieties

Simplifies previous proofs of the Torelli theorem

Abstract

In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.