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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 is a review of theory of toric Landau–Ginzburg models — the effective approach to mirror symmetry for Fano varieties. We mainly focus 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 Katzarkov–Kontsevich–Pantev conjectures, are also studied.

Keywords: Mirror Symmetry, toric Landau-Ginzburg models, Hodge numbers.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001


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

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English version:
DOI: https://doi.org/10.1070/RM9852

Document Type: Article
UDC: 512.7
MSC: 14J33; 14J45; 14M25; 52B20
Received: 10.09.2018

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

Citation in format AMSBIB
\Bibitem{Prz18}
\by V.~V.~Przyjalkowski
\paper Toric Landau--Ginzburg models
\jour Uspekhi Mat. Nauk
\yr 2018
\vol 73
\issue 6(444)
\pages 95--190
\mathnet{http://mi.mathnet.ru/umn9852}
\crossref{https://doi.org/10.4213/rm9852}
\elib{http://elibrary.ru/item.asp?id=36448088}


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