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This article is cited in 27 scientific papers (total in 27 papers)
On Kummer surfaces
V. V. Nikulin
Abstract:
In this paper we show that a Kähler $K3$ surface containing 16 nonsingular rational curves which do not intersect one another is a Kummer surface. We also give a direct proof of the global Torelli theorem for Kummer surfaces and develop a criterion for a surface to be Kummer which refines the criterion in the paper “A Torelli theorem for algebraic $K3$ surfaces” by I. I. Pyatetskii-Shapiro and I. R. Shafarevich.
Bibliography: 8 items.
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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:2, 261–275
Bibliographic databases:
 
Document Type:
Article
UDC:
513.6
MSC: Primary 14J10; Secondary 14J25
Received: 26.04.1974
Citation:
V. V. Nikulin, “On Kummer surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 278–293; Math. USSR-Izv., 9:2 (1975), 261–275
Citation in format AMSBIB
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\by V.~V.~Nikulin
\paper On Kummer surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 2
\pages 278--293
\mathnet{http://mi.mathnet.ru/izv1831}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=429917}
\zmath{https://zbmath.org/?q=an:0312.14008}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 2
\pages 261--275
\crossref{https://doi.org/10.1070/IM1975v009n02ABEH001477}
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http://mi.mathnet.ru/eng/izv1831 http://mi.mathnet.ru/eng/izv/v39/i2/p278
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This publication is cited in the following articles:
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K. Hulek, I. Nieto, G. K. Sankaran, “Heisenberg-invariant kummer surfaces”, Proc Edin Math Soc, 43:2 (2000), 425
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Kristina Frantzen, “Classification of K3-surfaces with involution and maximal symplectic symmetry”, Math Ann, 2010
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Adrian Clingher, Charles F. Doran, “Lattice polarized K3 surfaces and Siegel modular forms”, Advances in Mathematics, 231:1 (2012), 172
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A. Taormina, K. Wendland, “The overarching finite symmetry group of Kummer surfaces in the Mathieu group M 24”, J. High Energ. Phys, 2013:8 (2013)
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V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. Math., 77:5 (2013), 954–997
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Lei Zhang, “Surfaces with
$$p_g = q= 1$$
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$$K^2 = 7$$
K 2 = 7 and non-birational bicanonical maps”, Geom Dedicata, 2014 -
V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794
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Cheng M.C.N., Harrison S., “Umbral Moonshine and K3 Surfaces”, Commun. Math. Phys., 339:1 (2015), 221–261
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V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II”, Izv. Math., 80:2 (2016), 359–402
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Garbagnati A., Sarti A., “Kummer surfaces and K3 surfaces with $(\mathbb{Z} /2\mathbb{Z} )^4$ symplectic action”, Rocky Mt. J. Math., 46:4 (2016), 1141–1205
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V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816
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Schaffler L., “K3 Surfaces With Z(2)(2) Symplectic Action”, Rocky Mt. J. Math., 48:7 (2018), 2347–2383
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V. A. Krasnov, “Real Kummer surfaces”, Izv. Math., 83:1 (2019), 65–103
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Roulleau X., Sarti A., “Construction of Nikulin Configurations on Some Kummer Surfaces and Applications”, Math. Ann., 373:1-2 (2019), 597–623
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