Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev

Research output: Contribution to journalArticle

18 Scopus citations

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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