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Torelli theorem for surfaces with \(p_g=c_1^2=1\) and \(K\) ample and with certain type of automorphism. (English) Zbl 0507.14028


MSC:

14J15 Moduli, classification: analytic theory; relations with modular forms
14J25 Special surfaces

References:

[1] D. Burns and M. Rapoport : On the Torelli problems for Kählerian K-3 surfaces . Ann, scient. Éc. Norm. Sup. 4e sér. 8-2 (1975) 235-274. · Zbl 0324.14008 · doi:10.24033/asens.1287
[2] F. Catanese : Surfaces with K2 = pg = 1 and their period mapping. Proc. Summer Meeting on Algebraic Geometry , Copenhagen 1978, Lecture Notes in Math. No 732, Springer Verlag, 1-29. · Zbl 0423.14019
[3] A. Fujiki and S. Nakano ; Supplement to ”On the inverse of Monoidal Transformation” , Publ. R.I.M.S. Kyoto Univ. 7 (1972) 637-644. · Zbl 0234.32019 · doi:10.2977/prims/1195193401
[4] D. Gieseker : Global moduli for surfaces of general type . Invent. Math. 43 (1977) 233-282. · Zbl 0389.14006 · doi:10.1007/BF01390081
[5] P. Griffiths : Periods of integrals on algebraic manifolds I, II, III : Amer. J. Math. 90 (1968) 568-626; 805-865; Publ. Math. I.H.E.S. 38 (1970) 125-180. · Zbl 0212.53503 · doi:10.1007/BF02684654
[6] F.I. Kĭnev : A simply connected surface of general type for which the local Torelli theorem does not hold (Russian) . Cont. Ren. Acad. Bulgare des Sci. 30-3 (1977) 323-325. · Zbl 0363.14005
[7] E. Looijenga and C. Peters : Torelli theorems for Kähler K3 surfaces , Comp. Math. 42-2 (1981) 145-186. · Zbl 0477.14006
[8] I. Piateckiĭ-Šapiro and I.R. Šafarevič : A Torelli theorem for algebraic surfaces of type K-3 , Izv. Akad. Nauk. 35 (1971) 530-572.
[9] A.N. Todorov : Surfaces of general type with pg = 1 and (K, K) = 1. I , Ann. scient. Éc. Norm. Sup. 4e sér. 13-1 (1980) 1-21. · Zbl 0478.14030 · doi:10.24033/asens.1375
[10] S. Usui : Period map of surfaces with pg = c21= 1 and K ample . Mem. Fac. Sci. Kochi Univ. (Math.) 2 (1981) 37-73. · Zbl 0487.14007
[11] S. Usui : Effect of automorphisms on variation of Hodge structure . J. Math. Kyoto Univ. 21-4 (1981). · Zbl 0497.14003 · doi:10.1215/kjm/1250521907
[12] F. Catanese : The moduli and the global period mapping of surfaces with K2 = pg = 1: A counterexample to the global Torelli problem , Comp. Math. 41-3 (1980) 401-414. · Zbl 0444.14008
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