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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 813–852 (Mi izv1206)  

This article is cited in 22 scientific papers (total in 23 papers)

Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with $p_g>0$

A. N. Tyurin


Abstract: The author studies the geometry and the periods of components of moduli of sheaves on a regular algebraic surface.
Bibliography: 14 titles.

Full text: PDF file (4582 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 139–177

Bibliographic databases:

UDC: 516.5
MSC: 14J10, 14F05
Received: 17.11.1986

Citation: A. N. Tyurin, “Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with $p_g>0$”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 813–852; Math. USSR-Izv., 33:1 (1989), 139–177

Citation in format AMSBIB
\Bibitem{Tyu88}
\by A.~N.~Tyurin
\paper Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with~$p_g>0$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 813--852
\mathnet{http://mi.mathnet.ru/izv1206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966986}
\zmath{https://zbmath.org/?q=an:0673.14021}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 139--177
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000818}


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    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. A. N. Tyurin, “Algebraic geometric aspects of smooth structure. I. The Donaldson polynomials”, Russian Math. Surveys, 44:3 (1989), 113–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. N. Tyurin, “The Weil–Petersson metric on the moduli space of stable vector bundles and sheaves on an algebraic surface”, Math. USSR-Izv., 38:3 (1992), 599–620  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Zhenbo Qin, “Simple sheaves versus stable sheaves on algebraic surfaces”, Math Z, 209:1 (1992), 559  crossref  mathscinet  zmath  isi
    4. V. Ya. Pidstrigach, A. N. Tyurin, “Invariants of the smooth structure of an algebraic surface arising from the Dirac operator”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 267–351  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Zhenbo Qin, “Moduli of simple rank-2 sheaves onK3-surfaces”, manuscripta math, 79:1 (1993), 253  crossref  mathscinet  zmath
    6. Hoil Kim, “Exceptional bundles on nodal Enriques surfaces”, manuscripta math, 82:1 (1994), 1  crossref  mathscinet  zmath  isi
    7. A. N. Tyurin, “Canonical spin polynomials of an algebraic surface. I”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 577–621  mathnet  crossref  mathscinet  zmath  isi
    8. Angelo Felice Lopez, Gian Pietro Pirola, “On the curves through a general point of a smooth surface in ℙ3 ”, Math Z, 219:1 (1995), 93  crossref  mathscinet  zmath  isi
    9. Francesco Bottacin, “Poisson structures on moduli spaces of sheaves over Poisson surfaces”, Invent math, 121:1 (1995), 421  crossref  mathscinet  zmath  isi
    10. A. N. Tyurin, “Special Lagrangian geometry as slightly deformed algebraic geometry (geometric quantization and mirror symmetry)”, Izv. Math., 64:2 (2000), 363–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. A. N. Tyurin, “Non-abelian analogues of Abel's theorem”, Izv. Math., 65:1 (2001), 123–180  mathnet  crossref  crossref  mathscinet  zmath
    12. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. D. G. Markushevich, A. S. Tikhomirov, “Symplectic structure on a moduli space of sheaves on the cubic fourfold”, Izv. Math., 67:1 (2003), 121–144  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226  mathnet  mathscinet  zmath
    15. CLAUDIO BARTOCCI, EMANUELE MACRÌ, “CLASSIFICATION OF Poisson SURFACES”, Commun. Contemp. Math, 07:01 (2005), 89  crossref
    16. “STABLE VECTOR BUNDLES OF RANK TWO ON ENRIQUES SURFACES”, Journal of the Korean Mathematical Society, 43:4 (2006), 765  crossref
    17. Jacques Hurtubise, “Separation of Variables and the Geometry of Jacobians”, SIGMA, 3 (2007), 017, 14 pp.  mathnet  crossref  mathscinet  zmath
    18. Eyal Markman, “Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces”, Advances in Mathematics, 208:2 (2007), 622  crossref
    19. John Harnad, Jacques Hurtubise, “Multi-Hamiltonian structures for r-matrix systems”, J Math Phys (N Y ), 49:6 (2008), 062903  crossref  mathscinet  zmath  isi  elib
    20. C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. Math., 72:3 (2008), 497–508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    21. Kuznetsov, A, “Symplectic structures on moduli spaces of sheaves via the Atiyah class”, Journal of Geometry and Physics, 59:7 (2009), 843  crossref  isi  elib
    22. Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237  mathnet  crossref  mathscinet  zmath  isi  elib
    23. Francesco Sala, “Symplectic structures on moduli spaces of framed sheaves on surfaces”, centr.eur.j.math, 2012  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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