In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Bogomolov- 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 attracted to a potential in terms of mirror symmetry for one parameter families of symplectic Fano manifolds and argue that modulo a natural triviality property the moduli spaces of Landau-Ginzburg models posses canonical special coordinates.
|Original language||English (US)|
|Number of pages||63|
|Journal||Journal of Differential Geometry|
|State||Published - Jan 1 2017|
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology