Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)55-117
Number of pages63
JournalJournal of Differential Geometry
Volume105
Issue number1
StatePublished - Jan 1 2017
Externally publishedYes

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Ginzburg-Landau Model
Mirror Symmetry
Moduli Space
Theorem
Fano Manifolds
Hodge Theory
Symplectic Manifold
Ginzburg-Landau
Degeneration
Modulo
Smoothness
Necessary
Family

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models. / Katzarkov, Ludmil; Kontsevich, Maxim; Pantev, Tony.

In: Journal of Differential Geometry, Vol. 105, No. 1, 01.01.2017, p. 55-117.

Research output: Contribution to journalArticle

Katzarkov, L, Kontsevich, M & Pantev, T 2017, 'Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models', Journal of Differential Geometry, vol. 105, no. 1, pp. 55-117.
Katzarkov, Ludmil ; Kontsevich, Maxim ; Pantev, Tony. / Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models. In: Journal of Differential Geometry. 2017 ; Vol. 105, No. 1. pp. 55-117.
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