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January 2017 Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models
Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev
J. Differential Geom. 105(1): 55-117 (January 2017). DOI: 10.4310/jdg/1483655860

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.

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Ludmil Katzarkov. Maxim Kontsevich. Tony Pantev. "Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models." J. Differential Geom. 105 (1) 55 - 117, January 2017. https://doi.org/10.4310/jdg/1483655860

Information

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

zbMATH: 1361.35172
MathSciNet: MR3592695
Digital Object Identifier: 10.4310/jdg/1483655860

Rights: Copyright © 2017 Lehigh University

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Vol.105 • No. 1 • January 2017
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