Journal of Differential Geometry

Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models

Ludmil Katzarkov, Maxim Kontsevich, and Tony Pantev

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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.

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J. Differential Geom., Volume 105, Number 1 (2017), 55-117.

Received: 4 December 2014
First available in Project Euclid: 5 January 2017

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Katzarkov, Ludmil; Kontsevich, Maxim; Pantev, Tony. Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models. J. Differential Geom. 105 (2017), no. 1, 55--117. doi:10.4310/jdg/1483655860.

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