RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2007, Volume 198, Number 9, Pages 107–122 (Mi msb3913)  

This article is cited in 8 scientific papers (total in 8 papers)

Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties

V. V. Przyjalkowski

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Givental's theorem for complete intersections in smooth toric varieties is generalized to Fano varieties. The Gromov–Witten invariants are found for Fano varieties of dimension $\ge3$ that are complete intersections in weighted projective spaces or singular toric varieties. A generalized Riemann–Roch equation is also obtained for such varieties. As a consequence, the counting matrices of smooth Fano threefolds with Picard group $\mathbb Z$ and anticanonical degrees 2, 8, and 16 are calculated.
Bibliography: 29 titles.

DOI: https://doi.org/10.4213/sm3913

Full text: PDF file (666 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:9, 1325–1340

Bibliographic databases:

UDC: 512.772
MSC: 14J45, 14M25, 11F23
Received: 18.01.2005 and 07.09.2006

Citation: V. V. Przyjalkowski, “Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties”, Mat. Sb., 198:9 (2007), 107–122; Sb. Math., 198:9 (2007), 1325–1340

Citation in format AMSBIB
\Bibitem{Prz07}
\by V.~V.~Przyjalkowski
\paper Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 9
\pages 107--122
\mathnet{http://mi.mathnet.ru/msb3913}
\crossref{https://doi.org/10.4213/sm3913}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2360793}
\zmath{https://zbmath.org/?q=an:05272602}
\elib{https://elibrary.ru/item.asp?id=9557507}
\transl
\jour Sb. Math.
\yr 2007
\vol 198
\issue 9
\pages 1325--1340
\crossref{https://doi.org/10.1070/SM2007v198n09ABEH003885}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000252573100006}
\elib{https://elibrary.ru/item.asp?id=14638742}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849097203}


Linking options:
  • http://mi.mathnet.ru/eng/msb3913
  • https://doi.org/10.4213/sm3913
  • http://mi.mathnet.ru/eng/msb/v198/i9/p107

    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. Przyjalkowski V., “On Landau-Ginzburg models for Fano varieties”, Commun. Number Theory Phys., 1:4 (2007), 713–728  crossref  mathscinet  isi  elib  scopus
    2. V. V. Przyjalkowski, “Minimal Gromov–Witten rings”, Izv. Math., 72:6 (2008), 1253–1272  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Przyjalkowski V., “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
    4. V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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
    6. Coates T., Corti A., Galkin S., Kasprzyk A., “Quantum periods for 3–dimensional Fano manifolds”, Geom. Topol., 20:1 (2016), 103–256  crossref  mathscinet  zmath  isi  scopus
    7. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Przyjalkowski V., Shramov C., “Nef Partitions For Codimension 2 Weighted Complete Intersections”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 19:3 (2019), 827–845  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:402
    Full text:149
    References:54
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020