An algebraic proof of Bogomolov-Tian-Todorov theorem

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.

20 pages, amsproc

References in corpus (6)

• Deformation theory via differential graded Lie algebras
• Lectures on deformations of complex manifolds
• Transferring homotopy commutative algebraic structures
• Semicosimplicial DGLAs in deformation theory
• L-infinity algebras, Cartan homotopies and period maps
• Deformations via Simplicial Deformation Complexes

Cited by in corpus (15)

• Smoothing toroidal crossing spaces
• Deformations and obstructions of pairs (X,D)
• Semiregularity and obstructions of complete intersections
• Nonabelian higher derived brackets
• Period mappings for noncommutative algebras
• A period map for global derived stacks
• A short note on infinity-groupoids and the period map for projective manifolds
• The global derived period map
• Versality in mirror symmetry
• Connections and $L_{\infty }$ liftings of semiregularity maps
• On the abstract Bogomolov-Tian-Todorov Theorem
• Deformations of Calabi-Yau manifolds in Fano toric varieties
• Hochschild cohomology and deformations of $\mathbb{P}$-functors
• Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle)
• Logarithmic $\partial \bar{\partial }$-lemma and several geometric applications (with an Appendix joint with Sheng Rao)