Degenerations of K\"ahlerian K3 surfaces with finite symplectic automorphism groups.~III
Izvestiya. Mathematics , Tome 81 (2017) no. 5, pp. 985-1029.

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Following our papers [1] and [2] (Parts I and II), we classify degenerations of codimension 2 or more of Kählerian K3 surfaces with finite symplectic automorphism groups. In [1] and [2] this was done for codimension 1.
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.~III. Izvestiya. Mathematics , Tome 81 (2017) no. 5, pp. 985-1029. http://geodesic.mathdoc.fr/item/IM2_2017_81_5_a3/

[1] V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794 ; arXiv: 1403.6061 | DOI | DOI | MR | Zbl

[2] V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II”, Izv. Math., 80:2 (2016), 359–402 ; arXiv: 1504.00326 | DOI | DOI | MR | Zbl

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

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

[5] V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. II”, Development of moduli theory–Kyoto 2013, Adv. Stud. Pure Math., 69, Math. Soc. Japan, Tokyo, 2016, 421–471 ; arXiv: 1109.2879 | MR | Zbl

[6] V. V. Nikulin, Degenerations of Kählerian $\mathrm{K3}$ surfaces with finite symplectic automorphism groups. III, 2016, arXiv: 1608.04373

[7] Vik. S. Kulikov, “Plane rational quartics and K3 surfaces”, Proc. Steklov Inst. Math., 294 (2016), 95–128 | DOI | DOI | MR | Zbl

[8] I. R. Shafarevich, B. G. Averbukh, Yu. R. Vainberg, A. B. Zhizhchenko, Yu. I. Manin, B. G. Moishezon, G. N. Tyurina, A. N. Tyurin, “Algebraicheskie poverkhnosti”, Tr. MIAN SSSR, 75, Nauka, M., 1965, 3–215 | MR | Zbl

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

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

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

[12] 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

[13] 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

[14] V. V. Nikulin, “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa KZ”, UMN, 31:2(188) (1976), 223–224 | MR | Zbl

[15] V. V. Nikulin, “Finite automorphism groups of Kähler K3 surfaces”, Trans. Moscow Math. Soc., 2 (1980), 71–135 | MR | Zbl

[16] Sh. Mukai, “Finite groups of automorphisms of K3 surfaces and the Mathieu group”, Invent. Math., 94:1 (1988), 183–221 | DOI | MR | Zbl

[17] Gang Xiao, “Galois covers between $K3$ surfaces”, Ann. Inst. Fourier (Grenoble), 46:1 (1996), 73–88 | DOI | MR | Zbl

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

[19] GAP – Groups, Algorithms, Programming – a system for computational discrete algebra, Version 4.6.5, 2013 http://www.gap-system.org

[20] 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