RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 4, Pages 135–160 (Mi izv8018)  

This article is cited in 15 scientific papers (total in 15 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.

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


DOI: https://doi.org/10.4213/im8018

Full text: PDF file (691 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:4, 772–794

Bibliographic databases:

ArXiv: 0902.4668
Document Type: Article
UDC: 512.776
MSC: 14J33, 14J45, 14N35
Received: 26.06.2012
Revised: 15.10.2012

Citation: V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. RAN. Ser. Mat., 77:4 (2013), 135–160; Izv. Math., 77:4 (2013), 772–794

Citation in format AMSBIB
\Bibitem{Prz13}
\by V.~V.~Przyjalkowski
\paper Weak Landau--Ginzburg models for smooth Fano threefolds
\jour Izv. RAN. Ser. Mat.
\yr 2013
\vol 77
\issue 4
\pages 135--160
\mathnet{http://mi.mathnet.ru/izv8018}
\crossref{https://doi.org/10.4213/im8018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3135701}
\zmath{https://zbmath.org/?q=an:06216128}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013IzMat..77..772P}
\elib{http://elibrary.ru/item.asp?id=20425284}
\transl
\jour Izv. Math.
\yr 2013
\vol 77
\issue 4
\pages 772--794
\crossref{https://doi.org/10.1070/IM2013v077n04ABEH002660}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000323747900007}
\elib{http://elibrary.ru/item.asp?id=20457912}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884661155}


Linking options:
  • http://mi.mathnet.ru/eng/izv8018
  • https://doi.org/10.4213/im8018
  • http://mi.mathnet.ru/eng/izv/v77/i4/p135

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Przyjalkowski, “Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models”, Cent. Eur. J. Math., 9:5 (2011), 972–977  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. Gorbounov, V. Petrov, “Schubert calculus and singularity theory”, J. Geom. Phys., 62:2 (2012), 352–360  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. N. O. Ilten, J. Lewis, V. Przyjalkowski, “Degenerations of Fano threefolds giving weak Landau-Ginzburg models”, J. Algebra, 374 (2013), 104–121  crossref  mathscinet  zmath  isi  elib  scopus
    4. J. A. Christophersen, N. O. Ilten, “Degenerations to unobstructed Fano Stanley–Reisner schemes”, Math. Z., 278:1-2 (2014), 131–148  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. Iliev, L. Katzarkov, V. Przyjalkowski, “Double solids, categories and non-rationality”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 145–173  crossref  mathscinet  zmath  isi  scopus
    6. V. V. Przyjalkowski, C. A. Shramov, “Laurent phenomenon for Landau–Ginzburg models of complete intersections in Grassmannians”, Proc. Steklov Inst. Math., 290:1 (2015), 91–102  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. V. Gorbounov, M. Smirnov, “Some remarks on Landau-Ginzburg potentials for odd-dimensional quadrics”, Glasg. Math. J., 57:3 (2015), 481–507  crossref  mathscinet  zmath  isi  scopus
    8. G. Kapustka, “Projections of del Pezzo surfaces and Calabi-Yau threefolds”, Adv. Geom., 15:2 (2015), 143–158  crossref  mathscinet  zmath  isi  scopus
    9. T. Coates, A. Kasprzyk, T. Prince, “Four-dimensional Fano toric complete intersections”, Proc. of The Royal Society A. Math., Phys. and Eng. Sci., 471 (2015), 2175  crossref  mathscinet  zmath  elib  scopus
    10. V. V. Golyshev, D. Zagier, “Proof of the gamma conjecture for Fano 3-folds of Picard rank 1”, Izv. Math., 80:1 (2016), 24–49  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. C. Shramov, V. Przyjalkowski, “Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes”, Bull. Korean Math. Soc., 54:5 (2017), 1527–1575 , arXiv: 1409.3729  mathnet  crossref  mathscinet  isi  scopus
    13. 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
    14. V. Lunts, V. Przyjalkowski, “Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces”, Adv. Math., 329 (2018), 189–216  crossref  mathscinet  zmath  isi  scopus
    15. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:312
    Full text:39
    References:24
    First page:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019