An operadic proof of the BTT Theorem

TL;DR

This paper presents an operadic proof of the BTT Theorem, demonstrating that the deformation theory of Calabi-Yau varieties is unobstructed, and extends the proof to non-commutative cases and positive characteristic scenarios.

Contribution

It provides a novel operadic proof of the BTT Theorem and introduces new insights into non-commutative and positive characteristic cases.

Findings

Operadic proof of the BTT Theorem established

Unobstructed deformation theory of Calabi-Yau varieties confirmed

Partial results obtained in positive characteristic

Abstract

In this note, we explain an operadic proof of the BTT Theorem stating that the deformation theory of Calabi-Yau varieties is unobstructed. We also provide a short new proof of the non-commutative BTT for Calabi-Yau dg-categories. Finally, we observe that our proof also produces partial results in positive characteristic.