# Torelli theorem for surfaces with ${p}_{g}={c}_{1}^{2}=1$ and $K$ ample and with certain type of automorphism

Compositio Mathematica (1982)

- Volume: 45, Issue: 3, page 293-314
- ISSN: 0010-437X

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topUsui, Sampei. "Torelli theorem for surfaces with $p_g = c^2_1 = 1$ and $K$ ample and with certain type of automorphism." Compositio Mathematica 45.3 (1982): 293-314. <http://eudml.org/doc/89537>.

@article{Usui1982,

author = {Usui, Sampei},

journal = {Compositio Mathematica},

keywords = {moduli spaces; period mapping; automorphisms of surfaces; global Torelli theorem},

language = {eng},

number = {3},

pages = {293-314},

publisher = {Martinus Nijhoff Publishers},

title = {Torelli theorem for surfaces with $p_g = c^2_1 = 1$ and $K$ ample and with certain type of automorphism},

url = {http://eudml.org/doc/89537},

volume = {45},

year = {1982},

}

TY - JOUR

AU - Usui, Sampei

TI - Torelli theorem for surfaces with $p_g = c^2_1 = 1$ and $K$ ample and with certain type of automorphism

JO - Compositio Mathematica

PY - 1982

PB - Martinus Nijhoff Publishers

VL - 45

IS - 3

SP - 293

EP - 314

LA - eng

KW - moduli spaces; period mapping; automorphisms of surfaces; global Torelli theorem

UR - http://eudml.org/doc/89537

ER -

## References

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- [2] F. Catanese: Surfaces with K2 = pg = 1 and their period mapping. Proc. Summer Meeting on Algebraic Geometry, Copenhagen1978, Lecture Notes in Math. No 732, Springer Verlag, 1-29. Zbl0423.14019
- [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. Zbl0234.32019MR294712
- [4] D. Gieseker: Global moduli for surfaces of general type. Invent. Math.43 (1977) 233-282. Zbl0389.14006MR498596
- [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. Zbl0212.53503
- [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. Zbl0363.14005MR441981
- [7] E. Looijenga and C. Peters: Torelli theorems for Kähler K3 surfaces, Comp. Math.42-2 (1981) 145-186. Zbl0477.14006MR596874
- [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. MR284440
- [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. Zbl0478.14030
- [10] S. Usui: Period map of surfaces with pg = c21= 1 and K ample. Mem. Fac. Sci. Kochi Univ. (Math.)2 (1981) 37-73. Zbl0487.14007MR602105
- [11] S. Usui: Effect of automorphisms on variation of Hodge structure. J. Math. Kyoto Univ.21-4 (1981). Zbl0497.14003MR637511
- [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. Zbl0444.14008MR589089

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