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Izvestiya: Mathematics, 2013, Volume 77, Issue 4, Pages 772–794
DOI: https://doi.org/10.1070/IM2013v077n04ABEH002660
(Mi im8018)
 

This article is cited in 35 scientific papers (total in 35 papers)

Weak Landau–Ginzburg models for smooth Fano threefolds

V. V. Przyjalkowski

Steklov Mathematical Institute of the Russian Academy of Sciences
References:
Abstract: We consider Landau–Ginzburg models for smooth Fano threefolds of the principal series and prove that they can be represented by Laurent polynomials. We check that these models can be compactified to open Calabi–Yau varieties. In the spirit of Katzarkov's programme we prove that the numbers of irreducible components of the central fibres of compactifications of these pencils are equal to the dimensions of intermediate Jacobians of the corresponding Fano varieties plus 1. In particular, these numbers are independent of the choice of compactification. We state most of the known methods for finding Landau–Ginzburg models in terms of Laurent polynomials. We discuss the Laurent polynomial representation of the Landau–Ginzburg models of Fano varieties and state some related problems.
Keywords: weak Landau–Ginzburg models, Fano varieties, toric degeneration, intermediate Jacobian.
Funding agency Grant number
Austrian Science Fund P20778
Russian Foundation for Basic Research 11-01-00336-a
11-01-00185-a
12-01-31012
12-01-33024
Ministry of Education and Science of the Russian Federation МК-1192.2012.1
НШ-5139.2012.1
11.G34.31.0023
Dynasty Foundation
National Science Foundation DMS-0854977
DMS-0854977
DMS-0901330
Received: 26.06.2012
Revised: 15.10.2012
Bibliographic databases:
Document Type: Article
UDC: 512.776
MSC: 14J33, 14J45, 14N35
Language: English
Original paper language: Russian
Citation: V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794
Citation in format AMSBIB
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\by V.~V.~Przyjalkowski
\paper Weak Landau--Ginzburg models for smooth Fano threefolds
\jour Izv. Math.
\yr 2013
\vol 77
\issue 4
\pages 772--794
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\crossref{https://doi.org/10.1070/IM2013v077n04ABEH002660}
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Linking options:
  • https://www.mathnet.ru/eng/im8018
  • https://doi.org/10.1070/IM2013v077n04ABEH002660
  • https://www.mathnet.ru/eng/im/v77/i4/p135
  • This publication is cited in the following 35 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:669
    Russian version PDF:192
    English version PDF:25
    References:73
    First page:21
     
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