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) |
|---|---|
| Pages (from-to) | 55-117 |
| Number of pages | 63 |
| Journal | Journal of Differential Geometry |
| Volume | 105 |
| Issue number | 1 |
| State | Published - Jan 1 2017 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models
AU - Katzarkov, Ludmil
AU - Kontsevich, Maxim
AU - Pantev, Tony
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85009224948&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009224948&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85009224948
VL - 105
SP - 55
EP - 117
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
SN - 0022-040X
IS - 1
ER -