Torelli theorems for Kähler K3 surfaces

Eduard Looijenga; Chris Peters

Compositio Mathematica (1980)

  • Volume: 42, Issue: 2, page 145-186
  • ISSN: 0010-437X

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Looijenga, Eduard, and Peters, Chris. "Torelli theorems for Kähler K3 surfaces." Compositio Mathematica 42.2 (1980): 145-186. <http://eudml.org/doc/89474>.

@article{Looijenga1980,
author = {Looijenga, Eduard, Peters, Chris},
journal = {Compositio Mathematica},
keywords = {global Torelli theorem; kaehlerian K3 surfaces; Hodge structure; Kummer surfaces},
language = {eng},
number = {2},
pages = {145-186},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Torelli theorems for Kähler K3 surfaces},
url = {http://eudml.org/doc/89474},
volume = {42},
year = {1980},
}

TY - JOUR
AU - Looijenga, Eduard
AU - Peters, Chris
TI - Torelli theorems for Kähler K3 surfaces
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 42
IS - 2
SP - 145
EP - 186
LA - eng
KW - global Torelli theorem; kaehlerian K3 surfaces; Hodge structure; Kummer surfaces
UR - http://eudml.org/doc/89474
ER -

References

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  1. [1] M. Atiyah: On Analytic Surfaces with Double Points, Proc. Roy. Soc.A247 (1958) 237-244. Zbl0135.21301MR95974
  2. [2] E. Bishop: Conditions for the Analyticity of Certain Sets, Mich. Math. J.11 (1964) 283-304. Zbl0143.30302MR168801
  3. [3] N. Bourbaki: Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris1968. MR240238
  4. [4] D. Burns and M. Rapoport: On the Torelli Problems for Kählerian K-3 surfaces, Ann. Soc. de l'éc. N. Sup. 4e sér. 8 fase 2, 235-274 (1975). Zbl0324.14008MR447635
  5. [5] J. Dieudonne: La Géométrie der Groupes Classiques, Ergebnisse der Mathematik, Springer, Berlin (1955). Zbl0221.20056MR72144
  6. [6] F. Hirzebruch: Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlicher, Math. Ann.126, (1953) 1-22. Zbl0093.27605MR62842
  7. [7] F. Hirzebruch: Topological methods in algebraic geometry (3 rd edition), Springer, Berlin -Heidelberg-New York (1966). Zbl0138.42001MR202713
  8. [8] E. Horikawa: Surjectivity of the Period Map of K-3 surfaces of degree 2, Math. Ann., 228 (1977) 113-146. Zbl0333.32020MR460341
  9. [9] Ph. Griffiths:Periods of integrals on algebraic manifolds III, Publ. Math. IHES38 (1970) 125-180. Zbl0212.53503MR282990
  10. [10] H. Inose: On certain Kummer surfaces which can be realized as non-singular quartic surfaces in P3, J. Fac. Sci. Univ. Tokyo Sect. IA Math.23 no 3 (1976) 545-560. Zbl0344.14009MR429915
  11. [11] H. Inose and T. Shioda: On singular K-3 surfaces, in "Complex Analysis and Algebraic Geometry" A collection of Papers dedicated to K. Kodaira, Cambridge University Press (1977). Zbl0374.14006
  12. [12] K. Kodaira: On the structure of compact complex analytic surfaces, I, Am. J. Math.86 (1964) 751-798. Zbl0137.17501MR187255
  13. [13] K. Kodaira and D. Spencer: Existence of complex structure on a differentiable family of deformations of compact complex maniforlds, Ann. Math.70 (1959) 145-166. Zbl0124.16503MR112158
  14. [14] K. Kodaira and D. Spencer: On deformations of complex analytic structures III, Stability theorems for complex structures, Ann. Math71 (1960) 43-76. Zbl0128.16902MR115189
  15. [15] N. Kuranishi: On the locally complete families of complex analytic structures, Ann. Math.75 (1962) 536-577. Zbl0106.15303MR141139
  16. [16] V. Kulikov: Degenerations of K3 surfaces and Enriques surfaces, Izv. Akad. Nauk, Ser. Math., 41, no 5 (1977) 1008-1042. Zbl0387.14007MR506296
  17. [17] J. Milnor and D. Stasheff: Characteristic Classes, Ann of Math. Studies, 76, Princeton Univ. Press (1972). Zbl0298.57008
  18. [18] D. Mumford: Abelian Varieties, Oxford Univ. Press, Oxford (1970). Zbl0223.14022
  19. [19] V.V. Nikulin: On Kummer surfaces, Izv. Akad. Nauk SSSR, ser. Math., 39 (1975) 278-293. Zbl0312.14008MR429917
  20. [20] I. Piateckii-Shapiro and I.R. Safaravič: A Torelli Theorem for algebraic surfaces of type K-3, Izv. Akad. Nauk, 35(1971) 530-572. Zbl0219.14021
  21. [21] J.P. Serre: Cours d'Arithmétique, Presses Univ. de France, Paris (1970). Zbl0225.12002MR255476
  22. [22] J. Shah: Surjectivity of the Period Map in the case of quartic surfaces and sextic double planes, Bull. A.M.S., 82 (1976) 716-718. Zbl0339.14019MR417188
  23. [23] T. Shioda: The period map of abelian surfaces, J. Fac. Univ. Tokyo, 25, no 1 (1978) 47-59. Zbl0405.14021MR480530
  24. [24] T. Shioda and N. Mitani: Singular abelian surfaces and binary quadratic forms, in: Classification of algebraic varieties and compact complex manifolds, Springer Lecture Note in Math. 412, Springer Verlag, Berlin- Heidelberg-New York (1974). Zbl0302.14011MR382289
  25. [25] B. Saint-Donat: Projective models of K-3 surfaces, Am. J. Math.96 (1974) 602-639. Zbl0301.14011MR364263
  26. [26] A. Todorov: Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3-surfaces. Preprint (1979). Zbl0472.14006
  27. [27] E.B. Vinberg: Discrete groups generated by reflections, Izv. 35 no 5 (1971) 1083-1119. Zbl0256.20067MR302779

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