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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
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.
Received: 26.06.2012 Revised: 15.10.2012
Citation:
V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794
Linking options:
https://www.mathnet.ru/eng/im8018https://doi.org/10.1070/IM2013v077n04ABEH002660 https://www.mathnet.ru/eng/im/v77/i4/p135
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Abstract page: | 669 | Russian version PDF: | 192 | English version PDF: | 25 | References: | 73 | First page: | 21 |
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