Usui, Sampei Torelli theorem for surfaces with \(p_g=c_1^2=1\) and \(K\) ample and with certain type of automorphism. (English) Zbl 0507.14028 Compos. Math. 45, 293-314 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 14J15 Moduli, classification: analytic theory; relations with modular forms 14J25 Special surfaces Keywords:moduli spaces; period mapping; automorphisms of surfaces; global Torelli theorem Citations:Zbl 0444.14008; Zbl 0478.14030 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.