Abstract
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) |
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Pages (from-to) | 55-117 |
Number of pages | 63 |
Journal | Journal of Differential Geometry |
Volume | 105 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2017 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology