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



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






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


Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 1, Pages 131–158 (Mi izv421)  

This article is cited in 6 scientific papers (total in 6 papers)

Symplectic structure on a moduli space of sheaves on the cubic fourfold

D. G. Markushevich, A. S. Tikhomirov

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: We construct a 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold in the 5-dimensional projective space. It parametrizes the stable rank 2 vector bundles on hyperplane sections of the cubic 4-fold which are obtained by the Serre construction from normal elliptic quintics. The natural projection of this moduli space onto the dual projective 5-space is a Lagrangian fibration. The symplectic structure is closely related (and conjecturally equal) to the quasi-symplectic structure induced by the Yoneda pairing on the moduli space.

DOI: https://doi.org/10.4213/im421

Full text: PDF file (2360 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2003, 67:1, 121–144

Bibliographic databases:

UDC: 517.2
MSC: 14D20, 14J60, 14F05
Received: 10.09.2001

Citation: D. G. Markushevich, A. S. Tikhomirov, “Symplectic structure on a moduli space of sheaves on the cubic fourfold”, Izv. RAN. Ser. Mat., 67:1 (2003), 131–158; Izv. Math., 67:1 (2003), 121–144

Citation in format AMSBIB
\Bibitem{MarTik03}
\by D.~G.~Markushevich, A.~S.~Tikhomirov
\paper Symplectic structure on a~moduli space of sheaves on the cubic fourfold
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 1
\pages 131--158
\mathnet{http://mi.mathnet.ru/izv421}
\crossref{https://doi.org/10.4213/im421}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1957919}
\zmath{https://zbmath.org/?q=an:1075.14040}
\elib{https://elibrary.ru/item.asp?id=14364836}
\transl
\jour Izv. Math.
\yr 2003
\vol 67
\issue 1
\pages 121--144
\crossref{https://doi.org/10.1070/IM2003v067n01ABEH000421}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000185513200007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748500068}


Linking options:
  • http://mi.mathnet.ru/eng/izv421
  • https://doi.org/10.4213/im421
  • http://mi.mathnet.ru/eng/izv/v67/i1/p131

    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. Markushevich D.G., Tikhomirov A.S., “A parametrization of the theta divisor of the quartic double solid”, Int. Math. Res. Not., 2003, no. 51, 2747–2778  crossref  mathscinet  zmath  isi  elib
    2. Markushevich D., Tikhomirov A.S., “New symplectic $V$-manifolds of dimension four via the relative compactified Prymian”, Internat. J. Math., 18:10 (2007), 1187–1224  crossref  mathscinet  zmath  isi  elib  scopus
    3. Iliev A., Manivel L., “Cubic hypersurfaces and integrable systems”, Amer. J. Math., 130:6 (2008), 1445–1475  crossref  mathscinet  zmath  isi  elib  scopus
    4. Kuznetsov A., Markushevich D., “Symplectic structures on moduli spaces of sheaves via the Atiyah class”, J. Geom. Phys., 59:7 (2009), 843–860  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Kuznetsov A., Manivel L., Markushevich D., “Abel-Jacobi Maps for Hypersurfaces and Noncommutative Calabi-Yau's”, Communications in Contemporary Mathematics, 12:3 (2010), 373–416  crossref  mathscinet  zmath  isi  elib  scopus
    6. Laza R., Sacca G., Voisin C., “A Hyper-Kahler Compactification of the Intermediate Jacobian Fibration Associated With a Cubic 4-Fold”, Acta Math., 218:1 (2017), 55–135  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:312
    Full text:118
    References:25
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021