An algebraic proof of Bogomolov-Tian-Todorov theorem

TL;DR

This paper provides an entirely algebraic proof of the Bogomolov-Tian-Todorov theorem, demonstrating that the deformation theory of certain smooth projective varieties is governed by an abelian differential graded Lie algebra.

Contribution

It offers a new algebraic proof of the theorem, showing the governing L-infinity algebra is quasi-isomorphic to an abelian DGLA for varieties with trivial canonical bundle.

Findings

Deformation algebra is quasi-isomorphic to an abelian DGLA

Algebraic proof replaces previous analytic methods

Supports deformation unobstructedness for Calabi-Yau varieties

Abstract

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.