• Download PDF
• Download TeX
• Download bibTeX entry

Metadata

Abstract

References

[AC91] Auslander, Louis; Cook, Michael An algebraic classification of the three-dimensional crystallographic groups, Adv. Appl. Math., Volume 12 (1991) no. 1, pp. 1-21 | DOI | MR | Zbl

[AST11] Artebani, Michela; Sarti, Alessandra; Taki, Shingo $K3$ surfaces with non-symplectic automorphisms of prime order. With an appendix by Shigeyuki Kondō, Math. Z., Volume 268 (2011) no. 1-2, pp. 507-533 | DOI | MR | Zbl

[BEO02] Besche, Hans Ulrich; Eick, Bettina; O’Brien, Eamonn A. A millennium project: constructing small groups, Int. J. Algebra Comput., Volume 12 (2002) no. 5, pp. 623-644 | DOI | MR | Zbl

[BH19] Brandhorst, Simon; Hashimoto, Kenji Extensions of maximal symplectic actions on K3 surfaces (2019) (https://arxiv.org/abs/1910.05952)

[BHPVdV04] Barth, Wolf P.; Hulek, Klaus; Peters, Chris A. M.; Van de Ven, Antonius Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 4, Springer, 2004 | MR | Zbl

[BR75] Burns, Dan Jr.; Rapoport, Michael On the Torelli problem for kählerian K3 surfaces, Ann. Sci. Éc. Norm. Supér., Volume 8 (1975) no. 2, pp. 235-273 | DOI | MR | Zbl

[BS] Bonnafé, Cédric; Sarti, Alessandra Private communication

[BS19] Bonnafé, Cédric; Sarti, Alessandra K3 surfaces with maximal finite automorphism groups containing $M_{20}$ (2019) (https://arxiv.org/abs/1910.05955)

[CS99] Conway, John H.; Sloane, Neil J. A. Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften, 290, Springer, 1999 | MR | Zbl

[Dev19] Developers, The Sage SageMath, the Sage Mathematics Software System, 2019 (version 8.9), https://www.sagemath.org

[DGPS19] Decker, Wolfram; Greuel, Gert-Martin; Pfister, Gerhard; Schönemann, Hans Singular 4-1-2 — A computer algebra system for polynomial computations, http://www.singular.uni-kl.de, 2019

[Elk] Elkies, Noam D. Private communication

[Fra11] Frantzen, Kristina Classification of $K3$-surfaces with involution and maximal symplectic symmetry, Math. Ann., Volume 350 (2011) no. 4, pp. 757-791 | DOI | MR | Zbl

[Gro19] Group, The GAP GAP – Groups, Algorithms, and Programming,, 2019 (version 4.10.2, https://www.gap-system.org)

[Has11] Hashimoto, Kenji Period map of a certain $K3$ family with an ${𝔖}_{\mathfrak{5}}$-action, J. Reine Angew. Math., Volume 652 (2011), pp. 1-65 (With an appendix by Tomohide Terasoma) | DOI | MR | Zbl

[Has12] Hashimoto, Kenji Finite symplectic actions on the $K3$ lattice, Nagoya Math. J., Volume 206 (2012), pp. 99-153 | DOI | MR | Zbl

[HM16] Höhn, Gerald; Mason, Geoffrey The 290 fixed-point sublattices of the Leech lattice, J. Algebra, Volume 448 (2016), pp. 618-637 | DOI | MR | Zbl

[Huy16] Huybrechts, Daniel Lectures on K3 surfaces, Cambridge Studies in Advanced Mathematics, 158, Cambridge University Press, 2016 | DOI | MR | Zbl

[KK01] Keum, Jonghae; Kondō, Shigeyuki The automorphism groups of Kummer surfaces associated with the product of two elliptic curves, Trans. Am. Math. Soc., Volume 353 (2001) no. 4, pp. 1469-1487 | DOI | MR | Zbl

[Kon86] Kondō, Shigeyuki Enriques surfaces with finite automorphism groups, Jpn. J. Math., New Ser., Volume 12 (1986) no. 2, pp. 191-282 | DOI | MR | Zbl

[Kon98] Kondō, Shigeyuki Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of $K3$ surfaces. With an appendix by Mukai, Shigeru, Duke Math. J., Volume 92 (1998) no. 3, pp. 593-603 | Zbl

[Kon99] Kondō, Shigeyuki The maximum order of finite groups of automorphisms of $K3$ surfaces, Am. J. Math., Volume 121 (1999) no. 6, pp. 1245-1252 | DOI | MR | Zbl

[Kon06] Kondō, Shigeyuki Maximal subgroups of the Mathieu group $M_{23}$ and symplectic automorphisms of supersingular $K3$ surfaces, Int. Math. Res. Not. (2006), 71517 | DOI | MR | Zbl

[Kon18] Kondō, Shigeyuki A survey of finite groups of symplectic automorphisms of $K3$ surfaces, J. Phys. A, Math. Theor., Volume 51 (2018) no. 5, 053003 | DOI | MR | Zbl

[KOZ07] Keum, Jonghae; Oguiso, Keiji; Zhang, De-Qi Extensions of the alternating group of degree 6 in the geometry of $K3$ surfaces, Eur. J. Comb., Volume 28 (2007) no. 2, pp. 549-558 | DOI | MR | Zbl

[MO14] Mukai, Shigeru; Ohashi, Hisanori Finite groups of automorphisms of Enriques surfaces and the Mathieu group $M_{12}$ (2014) (https://arxiv.org/abs/1410.7535)

[Muk88] Mukai, Shigeru Finite groups of automorphisms of K3 surfaces and the Mathieu group, Invent. Math., Volume 94 (1988) no. 1, pp. 183-221 | DOI | MR | Zbl

[Nik79a] Nikulin, Vyacheslav V. Finite groups of automorphisms of Kählerian surfaces of type $K3$, Tr. Mosk. Mat. O.-va, Volume 38 (1979), pp. 75-137 | MR | Zbl

[Nik79b] Nikulin, Vyacheslav V. Integer symmetric bilinear forms and some of their geometric applications, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 43 (1979) no. 1, p. 111-177, 238 | MR

[Oha] Ohashi, Hisanori Private communication

[OZ02] Oguiso, Keiji; Zhang, De-Qi The simple group of order 168 and K3 surfaces, Complex geometry. Collection of papers dedicated to Hans Grauert on the occasion of his 70th birthday, Springer, 2002, pp. 165-184 | Zbl

[PAR18] PARI Group PARI/GP version 2.11.1, 2018 (available from http://pari.math.u-bordeaux.fr/)

[PS97] Plesken, Wilhelm; Souvignier, Bernd Computing isometries of lattices, J. Symb. Comput., Volume 24 (1997) no. 3-4, pp. 327-334 | DOI | MR | Zbl

[PTvdV92] Peters, Chris A. M.; Top, Jaap; van der Vlugt, Marcel The Hasse zeta function of a K3-surface related to the number of words of weight 5 in the Melas codes, J. Reine Angew. Math., Volume 432 (1992), pp. 151-176 | MR | Zbl

[PŠŠ71] Pjateckiĭ-Šapiro, Ilya I.; Šafarevič, Igor R. Torelli’s theorem for algebraic surfaces of type $\mathrm{K}3$, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 35 (1971), pp. 530-572 | MR

[Shi16] Shimada, Ichiro The automorphism groups of certain singular $K3$ surfaces and an Enriques surface, K3 surfaces and their moduli, Basel: Birkhäuser/Springer, 2016, pp. 297-343 | DOI | Zbl

[Shi20] Shimada, Ichiro The elliptic modular surface of level 4 and its reduction modulo 3, Ann. Mat. Pura Appl., Volume 199 (2020) no. 4, pp. 1457-1489 | DOI | MR | Zbl

[Smi07] Smith, James P. Picard-Fuchs Differential Equations for Families of K3 Surfaces (2007) (https://arxiv.org/abs/0705.3658)

[Tod80] Todorov, Andrei N. Applications of the Kähler–Einstein–Calabi–Yau metric to moduli of $K3$ surfaces, Invent. Math., Volume 61 (1980) no. 3, pp. 251-265 | DOI | MR | Zbl

[Uji13] Ujikawa, Masashi The automorphism group of the singular $K3$ surface of discriminant 7, Comment. Math. Univ. St. Pauli, Volume 62 (2013) no. 1, pp. 11-29 | MR | Zbl