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Russian Mathematical Surveys, 2018, Volume 73, Issue 6, Pages 1033–1118
DOI: https://doi.org/10.1070/RM9852 (Mi rm9852) 		 
This article is cited in 9 scientific papers (total in 9 papers)

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
English version PDF (1169 kB) Citations (9) Russian version article
References:
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DOI: https://doi.org/10.1070/RM9852
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.
Received: 10.09.2018
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: 14J33, 14J45
Language: English
Original paper language: Russian
Citation: V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    1. Claude Sabbah, Handbook of Geometry and Topology of Singularities VII, 2025, 327  crossref
    2. A. T. Fomenko, A. I. Shafarevich, V. A. Kibkalo, “Glavnye napravleniya i dostizheniya kafedry differentsialnoi geometrii i prilozhenii na sovremennom etape”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 27–37  mathnet  crossref  elib
    3. M. A. Ovcharenko, “On the existence of nef-partitions for smooth well-formed Fano weighted complete intersections”, Sib. elektron. matem. izv., 20:2 (2023), 1405–1419  mathnet  crossref  mathscinet
    4. A. Grassi, G. Gugiatti, W. Lutz, A. Petracci, “Reflexive polygons and rational elliptic surfaces”, Rend. Circ. Mat. Palermo, II. Ser., 72:6 (2023), 3185  crossref  mathscinet  zmath
    5. V. V. Przyjalkowski, “On singular log Calabi-Yau compactifications of Landau-Ginzburg models”, Sb. Math., 213:1 (2022), 88–108  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. V. V. Przyjalkowski, K. Rietsch, “Landau–Ginzburg models of complete intersections in Lagrangian Grassmannians”, Russian Math. Surveys, 76:3 (2021), 549–551  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. R. Kooistra, A. Thompson, “Threefolds fibred by mirror sextic double planes”, Can. J. Math.-J. Can. Math., 73:5 (2021), PII S0008414X20000498, 1305–1346  crossref  mathscinet  isi
    8. L. Katzarkov, V. V. Przyjalkowski, A. Harder, “P=W Phenomena”, Math. Notes, 108:1 (2020), 39–49  mathnet  crossref  crossref  mathscinet  isi  elib
    9. S. O. Gorchinskiy, D. V. Osipov, “Iterated Laurent series over rings and the Contou-Carrère symbol”, Russian Math. Surveys, 75:6 (2020), 995–1066  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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