Torelli theorem for surfaces with p g = c 1 2 = 1 and K ample and with certain type of automorphism

Sampei Usui

Compositio Mathematica (1982)

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

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Usui, 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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  1. [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. Zbl0324.14008MR447635
  2. [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. [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. [4] D. Gieseker: Global moduli for surfaces of general type. Invent. Math.43 (1977) 233-282. Zbl0389.14006MR498596
  5. [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. [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. [7] E. Looijenga and C. Peters: Torelli theorems for Kähler K3 surfaces, Comp. Math.42-2 (1981) 145-186. Zbl0477.14006MR596874
  8. [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. [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. [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. [11] S. Usui: Effect of automorphisms on variation of Hodge structure. J. Math. Kyoto Univ.21-4 (1981). Zbl0497.14003MR637511
  12. [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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