Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

@article{Katzarkov2014BogomolovTianTodorovTF,
  title={Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models},
  author={Ludmil Katzarkov and Maxim Kontsevich and Tony Pantev},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
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… 

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