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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 6(444), Pages 95–190 (Mi umn9852)  

Toric Landau–Ginzburg models

V. V. Przyjalkowskiab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University "Higher School of Economics", Moscow

Abstract: This review of the theory of toric Landau–Ginzburg models describes an effective approach to mirror symmetry for Fano varieties. It focuses mainly on the cases of dimensions 2 and 3, as well as on the case of complete intersections in weighted projective spaces and Grassmannians. Conjectures that relate invariants of Fano varieties and their Landau–Ginzburg models, such as the Katzarkov–Kontsevich–Pantev conjectures, are also studied.
Bibliography: 89 titles.

Keywords: toric Landau–Ginzburg models, mirror symmetry, toric geometry, Fano varieties.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
This research was carried out with the support of the Laboratory for Mirror Symmetry and Automorphic Forms, National Research Institute Higher School of Economics, RF Government grant, ag. no. 14.641.31.0001. The author is a winner of the “Young Russian Mathematics” prize and is grateful to the sponsors and jury of that competition.


DOI: https://doi.org/10.4213/rm9852

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English version:
Russian Mathematical Surveys, 2018, 73:6, 1033–1118

Bibliographic databases:

Document Type: Article
UDC: 512.7
MSC: 14J33, 14J45
Received: 10.09.2018

Citation: V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Uspekhi Mat. Nauk, 73:6(444) (2018), 95–190; Russian Math. Surveys, 73:6 (2018), 1033–1118

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