Geodesic
Degenerations of K\"ahlerian K3 surfaces with finite symplectic automorphism groups. II
Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 359-402.

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We prove the main conjecture (Conjecture 7.1) of the paper [1]. Using this result, we classify degenerations of codimension 1 of Kählerian K3 surfaces with finite symplectic automorphism groups.
Keywords: K3 surface, Kählerian surface, degeneration, singularities, Picard lattice, integral symmetric bilinear form.
Mots-clés : automorphism group 
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V. V. Nikulin. Degenerations of K\"ahlerian K3 surfaces with finite symplectic automorphism groups. II. Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 359-402. http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a5/

[1] V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794 | DOI | DOI | MR | Zbl

[2] V. V. Nikulin, “On Kummer surfaces”, Math. USSR-Izv., 9:2 (1975), 261–275 | DOI | MR | Zbl

[3] V. V. Nikulin, “Finite automorphism groups of Kähler $K3$ surfaces”, Trans. Moscow Math. Soc., 2, Amer. Math. Soc., Providence, RI, 1980, 71–135 | MR | Zbl

[4] V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167 | DOI | MR | Zbl

[5] V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172 | DOI | MR | Zbl

[6] V. V. Nikulin, Kahlerian K3 surfaces and Niemeier lattices, arXiv: 1109.2879

[7] V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. Math., 77:5 (2013), 954–997 | DOI | DOI | MR | Zbl

[8] K. Hashimoto, “Finite symplectic actions on the $K3$ lattice”, Nagoya Math. J., 206 (2012), 99–153 ; arXiv: 1012.2682 | DOI | MR | Zbl

[9] R. Miranda, D. R. Morrison, “The number of embeddings of integral quadratic forms. I”, Proc. Japan Acad. Ser. A Math. Sci., 61:10 (1985), 317–320 | DOI | MR | Zbl

[10] R. Miranda, D. R. Morrison, “The number of embeddings of integral quadratic forms. II”, Proc. Japan Acad. Ser. A Math. Sci., 62:1 (1986), 29–32 | DOI | MR | Zbl

[11] D. G. James, “The number of embeddings of quadratic $\mathbb Z$-lattices”, J. Number Theory, 58:1 (1996), 1–8 | DOI | MR | Zbl

[12] V. V. Nikulin, Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II, arXiv: 1504.00326

[13] I. R. Shafarevich, B. G. Averbukh, J. R. Vaĭnberg, A. B. Zhizhchenko, Yu. I. Manin, B. G. Moĭshezon, G. N. Tyurina, A. N. Tyurin, Algebraic surfaces, Proc. Steklov Inst. Math., 75, Amer. Math. Soc., Providence, R.I., 1967, 281 pp. | MR | Zbl

[14] I. I. Pjateckiĭ-S̆apiro, I. R. S̆afarevic̆, “A Torelli theorem for algebraic surfaces of type K3”, Math. USSR-Izv., 5:3 (1971), 547–588 | DOI | MR | Zbl

[15] D. Burns, M. Rapoport, “On the Torelli problem for kählerian $K$-3 surfaces”, Ann. Sci. École Norm. Sup. (4), 8:2 (1975), 235–273 | MR | Zbl

[16] Yum-Tong Siu, “A simple proof of the surjectivity of the period map of K3 surfaces”, Manuscripta Math., 35:3 (1981), 311–321 | DOI | MR | Zbl

[17] A. N. Todorov, “Applications of the Kähler–Einstein–Calabi–Yau metric to moduli of K3 surfaces”, Invent. Math., 61:3 (1980), 251–265 | DOI | MR | Zbl

[18] J. H. Conway, N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren Math. Wiss., 290, Springer-Verlag, New York, 1988, xxviii+663 pp. | DOI | MR | MR | MR | Zbl

[19] Vik. S. Kulikov, “Degenerations of $K3$ surfaces and Enriques surfaces”, Math. USSR-Izv., 11:5 (1977), 957–989 | DOI | MR | Zbl

[20] GAP – Groups, Algorithms, Programming – a system for computational discrete algebra, Version 4.6.5, 2013