Applications of the Kaehler-Einstein-Calabi-Yau metric to moduli of K3 surfaces. (English) Zbl 0472.14006


14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14J15 Moduli, classification: analytic theory; relations with modular forms
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
14D20 Algebraic moduli problems, moduli of vector bundles
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32G13 Complex-analytic moduli problems
14J25 Special surfaces
32J15 Compact complex surfaces
Full Text: DOI EuDML


[1] [AHS] Atiyah M., Hitchin, N., Singer, I.: Self-duality in four dimensional Riemannian geometry, Proc. Rot. Soc. Lond. Ser. A362, 425-461 · Zbl 0389.53011
[2] [B] Berger, M.: Sur quelques varietes d’Einstein compactes, Ann. Mat. Pura Appl.53, 89-95 (1961) · Zbl 0115.39301
[3] [BR] Burns, D., Rapoport, M.: On The Torelli problems for Kählerian K3 surfaces, Ann. Sci. Ecole Norm. Sup.4, ser, 8 f.2 (1975) · Zbl 0324.14008
[4] [H] Hitchin, N.: Compact four dimensional Einstein manifolds. J. Differential Geometry9, 435-441 (1974) · Zbl 0281.53039
[5] [LP] Looijenga, E., Peters, C.: Torelli theorems for Kähler K3 surfaces, preprint
[6] [KM] Morrow J., Kodaira, K.: Complex Manifolds Holt, Rinehart and Winston, Inc. (1971)
[7] [PP] Persson, U., Pinkham, H.: Degeneration of surfaces with trivial canonical bundle, preprint · Zbl 0426.14015
[8] [Sh] Safarevich, I.R.: Algebraic surfaces, Proc. Steklov Inst. Math. V. 75. (1965)
[9] [SP] Safarevich, I.R., Shapiro-Piateski, A.: A Torelli theorem for algebraic surfaces of type K3. Izv. Akad. Nauk35, 530-572 (1971)
[10] [S] Serre, J.-P.: Cours d’Arithmetique, Paris: Presses Universitaires de France 1970
[11] [ST] Singer, Thorpe: Global Analisis, papers in honor of K. Kodaira, pp. 355-365. Princeton University Press, 1969
[12] [WELLS] Wells, R.O.: Differential Analisis on Complex manifolds, Englewood Cliffs, N.J.: Prentice-Hall, 1973 · Zbl 0262.32005
[13] [Y] Yau, S.T.: On the ricci curvature of a compact Kähler manifolds and the Monge-Amper equation I Comm. Pure Appl. Math.XXXI, 339-411 (1978) · Zbl 0369.53059
[14] [K] Kulikov, V.: The surjectivity of the period map for algebraic K3 surfaces YMH32, 257-258 (1977) · Zbl 0449.14008
[15] [W] Weil, A.: Collected papers, vol.2, pp. 393-395, Berlin-Heidelberg-New York: Springer-Verlag 1979
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