An algebraic proof of Bogomolov-Tian-Todorov theorem

The logarithmic Bogomolov-Tian-Todorov theorem

We prove that the log smooth deformations of a proper log smooth saturated log Calabi-Yau space are unobstructed.

On the abstract Bogomolov-Tian-Todorov Theorem

We describe an abstract version of the Theorem of Bogomolov-Tian-Todorov, whose underlying idea is already contained in various papers by Bandiera, Fiorenza, Iacono, Manetti. More explicitly, we prove an algebraic criterion for a differential graded Lie algebras to be homotopy abelian. Then, we collect together many examples and applications in deformation theory and other settings.

Bogomolov-Tian-Todorov theorem for Calabi-Yau categories

We prove a generalization of Bogomolov-Tian-Todorov theorem to Calabi-Yau categories.

The Bogomolov-Tian-Todorov Theorem Of Cyclic $A_\infty$-Algebras

Let $A$ be a finite-dimensional smooth unital cyclic $A_\infty$-algebra. Assume furthermore that $A$ satisfies the Hodge-to-de-Rham degeneration property. In this short note, we prove the non-commutative analogue of the Bogomolov-Tian-Todorov theorem: the deformation functor associated with the differential graded Lie algebra of Hochschild cochains of $A$ is smooth. Furthermore, the deformation functor associated with the DGLA of cyclic Hochschild cochains of $A$ is also smooth.

Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the necessary Hodge theory for varieties with potentials, and prove a double degeneration statement needed for the unobstructedness result. We discuss the various definitions of Hodge numbers for non-commutative Hodge structures of Landau-Ginzburg type and the role they play in mirror symmetry. We also interpret the resulting families of de Rham complexes attacted to a potential in terms of mirror symmetry for…

全局对数形变理论

Global logarithmic deformation theory

本书探讨对数Bogomolov--Tian--Todorov定理的新证明方法，建立更强的抽象无阻碍性定理，并将其应用于对数平滑与轻度对数奇异空间的全局形变理论，获得对数卡拉比-丘空间等的无阻碍性结果。