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J. Algebra, 2013, Volume 374, Pages 104–121 (Mi ja6)  

This article is cited in 2 scientific papers (total in 2 papers)

Toric degenerations of Fano threefolds giving weak Landau–Ginzburg models

N. O. Iltena, J. Lewisb, V. Przyjalkowskic

a Dept. of Mathematics, University of California, Berkeley, CA 94720, United States
b Fakultät für Mathematik, Universität Wien, Garnisongasse 3/14, A-1090 Wien, Austria
c Steklov Mathematical Institute, Gubkina st., 8, 119991, Moscow, Russia

Abstract: We show that every Picard rank one smooth Fano threefold has a weak Landau–Ginzburg model coming from a toric degeneration. The fibers of these Landau–Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau–Ginzburg model coming from a toric degeneration.

Funding Agency Grant Number
Max-Planck-Institut für Mathematik
National Science Foundation DMS-0854977
DMS-0854977
DMS-0901330
OISE-0965183
Austrian Science Fund P 24572-N25
P20778
Russian Foundation for Basic Research 11-01-00336
11-01-00185
12-01-31012
Ministry of Education and Science of the Russian Federation MK-1192.2012.1
NSh- 5139.2012.1
11.G34.31.0023
Dynasty Foundation
N.I. was supported by the Max-Planck-Institut für Mathematik. V.P. was partially supported by NSF FRG DMS-0854977, NSF DMS-0854977, NSF DMS-0901330, grants FWF P 24572-N25 and FWF P20778, RFFI grants 11-01-00336-a, 11-01-00185-a, and 12-01-31012, grants MK-1192.2012.1, NSh-5139.2012.1, and AG Laboratory GU-HSE, RF government grant, ag. 11 11.G34.31.0023. J.L. was supported by NSF grant OISE-0965183. The paper was partially written during the first authorís visit to Moscow with support from the Dynasty Foundation.


DOI: https://doi.org/10.1016/j.jalgebra.2012.11.002


Bibliographic databases:

Document Type: Article
MSC: 14J33, 14J45, 14M25, 32G20, 14J28
Received: 13.08.2011
Language: English

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Przyjalkowski, “On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections”, Math. Notes, 103:1 (2018), 104–110  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  adsnasa  isi  elib
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