The automorphism groups of kummer surfaces associated with the product of two elliptic curves

Transactions of the American Mathematical Society

Volumn 353, Issue 4, 2001, Pages 1469-1487

  Keum, Jonghae ^a,c   Kondo, Shigeyuki ^a,b  

^a Konkuk University   (South Korea)

^b Korea Institute for Advanced Study   (South Korea)

^c NAGOYA UNIVERSITY   (Japan)

Author keywords

Automorphisms of kummer surfaces; Leech lattice; Picard lattice

Indexed keywords

EID: 23044526313     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02631-3     Document Type: Article

References (17)

1. R. Borcherds, Automorphism groups of Lorentzian lattices, 3. Algebra 111 (1987), 133-153. MR 89b:20018
2. J. H. Comvay, Three lectures on exceptional groups, in Finite simple groups, Academic Press, 1971, pp. 215-247. MR 49:2918
3. J. H. Comvay, The automorphism group of the 26 dimensional even Lorentzian lattice, J. Algebra 80 (1983), 159-163. MR 85k:11030
4. J. H. Comvay, N.J.A. Sloane, Sphere packings, lattices and groups, Grundlehren Math. Wiss. Bd 290, 2nd ed. 80 (1988). MR 89a:11067
5. J. H. Keum, Automorphisms of Jacobian Kummer surfaces, Compositio Math. 107 (1997), 269-288. MR 98e:14039
6. J. H. Keum, Every algebraic Kummer surface has infinitely many automorphisms, unpublished manuscript (1996).
7. S. Kondō, Enriques surfaces with finite automorphism groups, Japanese J. Math. 12 (1986), 191-282. MR 89c:14058
8. S. Kondō, The automorphism group of a generic Jacobian Kummer surface, J. Algebraic Geometry 7 (1998), 589-609. MR 991:14043
9. S. Kondō, The maximum order affinité groups of automorphisms of K3 surfaces, Amer. J. Mathematics 121 (1999), 1245-1252.
10. S. Mukai, Y. Namikawa, Automorphisms of Enriques surfaces which act trivially on cohomology groups, Invent, math. 77 (1984), 383-397. MR 861:14012
11. V.V. Nikulin, Finite groups of automorphisms of Kählerian surfaces of type K3, Moscow Math. Soc. 38 (1980), 71-137. MR 81e:32033
12. V.V. Nikulin, Integral symmetric bilinear forms and their applications, Math. USSR Izv. 14 (1980), 103-167. MR 80j:10031
13. I. Piatetski-Shapiro, I.R. Shafarevich, A Torelli theorem for algebraic surfaces of type K3, Math. USSR Izv. 5 (1971), 547-587. MR 44:1666
14. T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20-59. MR 55:2927
15. T. Shioda, H. Inose, On singular K3 surfaces, Complex analysis and algebraic geometry (Collection Dedicated to K. Kodaira), Iwanami Shoten, Tokyo, and Cambridge Univ. Press, Cambridge (1977), 119-136. MR 56:371
16. 24 as a collineation group, Ann. Mat. Pure Appl. 71 (1966), 199-238. MR 34:2713
17. E.B. Vinberg, Some arithmetic discrete groups in Lobachevskii spaces, in Proc. Int. Coll. on Discrete Subgroups of Lie Groups and appl. to Moduli (Bombay 1973), Oxford Univ. Press, 1975., pp. 323-348. MR 54:10492