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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 3, Pages 530–572 (Mi izv2021)  

This article is cited in 69 scientific papers (total in 70 papers)

A Torelli theorem for algebraic surfaces of type $K3$

I. I. Pyatetskii-Shapiro, I. R. Shafarevich


Abstract: In this paper it is proved that an algebraic surface of type $K3$ is uniquely determined by prescribing the integrals of its holomorphic differential forms with respect to a basis of cycles of the two-dimensional homology group, if the homology class of a hyperplane section is distinguished.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:3, 547–588

Bibliographic databases:

UDC: 513.6
MSC: Primary 14C30, 14D20, 14J10; Secondary 10B10, 14G99
Received: 26.01.1970

Citation: I. I. Pyatetskii-Shapiro, I. R. Shafarevich, “A Torelli theorem for algebraic surfaces of type $K3$”, Izv. Akad. Nauk SSSR Ser. Mat., 35:3 (1971), 530–572; Math. USSR-Izv., 5:3 (1971), 547–588

Citation in format AMSBIB
\Bibitem{PyaSha71}
\by I.~I.~Pyatetskii-Shapiro, I.~R.~Shafarevich
\paper A~Torelli theorem for algebraic surfaces of type~$K3$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 3
\pages 530--572
\mathnet{http://mi.mathnet.ru/izv2021}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=284440}
\zmath{https://zbmath.org/?q=an:0219.14021}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 3
\pages 547--588
\crossref{https://doi.org/10.1070/IM1971v005n03ABEH001075}


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    This publication is cited in the following articles:
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    17. S. P. Demushkin, A. I. Kostrikin, S. P. Novikov, A. N. Parshin, L. S. Pontryagin, A. N. Tyurin, D. K. Faddeev, “Igor' Rostislavovich Shafarevich (on his sixtieth birthday)”, Russian Math. Surveys, 39:1 (1984), 189–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    24. Amit Giveon, Dirk-Jan Smith, “Symmetries on the moduli space of (2,2) superstring vacua”, Nuclear Physics B, 349:1 (1991), 168  crossref
    25. Paul S Aspinwall, Mark Gross, “Heterotic-heterotic string duality and multiple K3 fibrations”, Physics Letters B, 382:1-2 (1996), 81  crossref
    26. Gritsenko V.A., Nikulin V.V., “Automorphic forms and Lorentzian Kac-Moody algebras. Part II”, International Journal of Mathematics, 9:2 (1998), 201–275  crossref  isi  elib
    27. S. Kondo, “A complex hyperbolic structure for the moduli space of curves of genus three”, crll, 2000:525 (2000), 219  crossref  mathscinet  zmath
    28. 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
    29. V. V. Nikulin, “On the Classification of Hyperbolic Root Systems of Rank Three”, Proc. Steklov Inst. Math., 230:3 (2000), 1–241  mathnet  mathscinet  zmath
    30. Gritsenko V.A., Nikulin V.V., “The arithmetic mirror symmetry and Calabi-Yau manifolds”, Communications in Mathematical Physics, 210:1 (2000), 1–11  crossref  isi  elib
    31. Degtyarev A., Itenberg I., Kharlamov V., “Real Enriques Surfaces”, Real Enriques Surfaces, Lect. Notes Math., 1746, Springer-Verlag Berlin, 2000, VII+  isi
    32. K. KOIKE, H. SHIGA, N. TAKAYAMA, T. TSUTSUI, “STUDY ON THE FAMILY OF K3 SURFACES INDUCED FROM THE LATTICE (D4)3⊕ <-2> ⊕ < 2>: STUDY ON THE FAMILY OF K3 SURFACES”, Int. J. Math, 12:09 (2001), 1049  crossref
    33. C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153  mathnet  mathscinet  zmath
    34. D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226  mathnet  mathscinet  zmath
    36. Degtyarev A., Itenberg I., Kharlamov V., “Finiteness and quasi-simplicity for symmetric K3-surfaces”, Duke Mathematical Journal, 122:1 (2004), 1–49  crossref  isi
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    38. Catanese F., “QED for algebraic varieties”, Journal of Differential Geometry, 77:1 (2007), 43–75  isi
    39. V. V. Nikulin, “On the connected components of moduli of real polarized K3-surfaces”, Izv. Math., 72:1 (2008), 91–111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    40. C.-Y. Chi, S.-T. Yau, “A geometric approach to problems in birational geometry”, Proc Natl Acad Sci, 105:48 (2008), 18696  crossref  mathscinet  adsnasa  isi
    41. 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
    42. Macri E., Stellari P., “Automorphisms and autoequivalences of generic analytic K3 surfaces”, Journal of Geometry and Physics, 58:1 (2008), 133–164  crossref  isi
    43. Macri E., Stellari P., “Infinitesimal Derived Torelli Theorem for K3 Surfaces (with an Appendix by Sukhendu Mehrotra)”, Internat Math Res Notices, 2009, no. 17, 3190  crossref  isi
    44. Huybrechts D., “The Global Torelli Theorem: Classical, Derived, Twisted”, Proceedings of Symposia in Pure Mathematics: Algebraic Geometry Seattle 2005, Vol 80, Pts 1 and 2, Proceedings of Symposia in Pure Mathematics, 80, eds. Abramovich D., Bertram A., Katzarkov L., Pandharipande R., Thaddeus M., Amer Mathematical Soc, 2009, 235–258  isi
    45. Artebani M., Hausen J., Laface A., “On Cox rings of K3 surfaces”, Compositio Math., 2010  crossref
    46. Evis Ieronymou, “Diagonal quartic surfaces and transcendental elements of the Brauer group”, JMJ, 2010, 1  crossref
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    48. Ekaterina Amerik, “On an automorphism of Hilb[2] of certain K3 surfaces”, Proceedings of the Edinburgh Mathematical Society, 54:01 (2011), 1  crossref
    49. Isao Naruki, Daisuke Tarama, “Algebraic geometry of the eigenvector mapping for a free rigid body”, Differential Geometry and its Applications, 2011  crossref
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    51. Jason Hadnot, “Differential geometry of the Fermat quartic and theta functions”, Journal of Geometry and Physics, 62:2 (2012), 137  crossref
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    63. Nikulin V.V., “Kahlerian K3 Surfaces and Niemeier Lattices, II”, Development of Moduli Theory - Kyoto 2013, Advanced Studies in Pure Mathematics, 69, ed. Fujino O. Kondo S. Moriwaki A. Saito M. Yoshioka K., Math Soc Japan, 2016, 421–471  mathscinet  isi
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