On K3 surfaces with large Picard number. (English) Zbl 0509.14034


14J10 Families, moduli, classification: algebraic theory
14J15 Moduli, classification: analytic theory; relations with modular forms
32J15 Compact complex surfaces
Full Text: DOI EuDML


[1] Burns, D., Rapoport, M.: On the Torelli problem for Kählerian K3 surfaces. Ann. Scient. Ec. Norm. Sup.8, 235-274 (1975) · Zbl 0324.14008
[2] Hodge, W.V.D.: The topological invariants of algebraic varieties. Proc. Intern. Cong. Math. Cambridge1, 182-192 (1950) · Zbl 0037.22301
[3] Kneser, M.: Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. Arch. Math. (Basel)7, 323-332 (1956) · Zbl 0071.27205
[4] Kodaira, K.: On the structure of compact complex analytic surface, I. Amer. J. Math.86, 751-798 (1964) · Zbl 0137.17501
[5] Kulikov, V.: Epimorphicity of the period mapping for surfaces of type K3., (in Russian) Uspehi Mat. Nauk.32, (4) 257-258 (1977) · Zbl 0449.14008
[6] Looijenga, E.: A Torelli theorem for Kähler-Einstein K3 surfaces. Lecture Notes in Mathematics, vol. 894, 107-112. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0473.53041
[7] Looijenga, E., Peters, C.: Torelli theorems for Kähler K3 surfaces. Compositio Math.42, 145-186 (1981) · Zbl 0477.14006
[8] Milnor, J.: On simply connected 4-manifolds. Symposium Internacional de Topologia Algebraica, La Universidad Nacional Autónoma de México y la UNESCO pp. 122-128, 1958
[9] Namikawa, Y.: Surjectivity of period map for K3 surfaces. Classification of algebraic and analytic manifolds, Progress in Mathematics, vol. 39, 379-397, Boston-Basel-Stuttgart: Birkhäuser 1983 · Zbl 0522.32023
[10] Nikulin, V.: On Kummer surfaces. Izv. Akad. Nauk SSSR39, 278-293 (1975); Math. USSR Izvestija9, 261-275 (1975)
[11] Nikulin, V.: Finite groups of automorphisms of Kählerian surfaces of type K3. Trudy Mosk. Mat. Ob.38, 75-137 (1979), Trans. Moscow Math. Soc.38, 71-135 (1980) · Zbl 0433.14024
[12] Nikulin, V.: Integral symmetric bilinear forms and some of their applications. Izv. Akad. Nauk SSSR43, 111-177 (1979), Math. USSR Izvestija14, 103-167 (1980) · Zbl 0408.10011
[13] Oda, T.: A note on the Tate conjecture for K3 surfaces. Proc. Japan. Acad. Ser A56, 296-300 (1980) · Zbl 0459.14003
[14] Okamoto, M.: On a certain decomposition of 2-dimenional cycles on a product of two algebraic surfaces. Proc. Japan Acad. Ser A57, 321-325 (1981) · Zbl 0529.14006
[15] Piateckii-Shapiro, I., Shafarevich, I.R.: A Torelli theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR35, 530-572 (1971); Math. USSR Izvestija5, 547-587 (1971) · Zbl 0219.14021
[16] Shafarevich, I.R., ed.: Algebraic surfaces. Proc. Steklov Institute of Math.75, (1965) · Zbl 0154.21001
[17] Shioda, T.: The period map of abelian surfaces. J. Fac. Sci. Univ. Tokyo25, 47-59 (1978) · Zbl 0405.14021
[18] Shioda, T., Inose, H.: On singular K3 surfaces. Complex analysis and algebraic geometry: papers dedicated to K. Kodaira. Iwanami Shoten and Cambridge University Press 1977, pp. 119-136
[19] Siu, Y.-T.: A simple proof of the surjectivity of the period map of K3 surfaces. Manuscripta math.35, 311-321 (1981) · Zbl 0497.32019
[20] Siu, Y.-T.: Every K3 surface is Kähler. Invent. math.73, 139-150 (1983) · Zbl 0557.32004
[21] Todorov, A.: Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces. Invent. math.61, 251-265 (1980) · Zbl 0472.14006
[22] Wu, W.T.: Classes caractéristiques eti-carrés d’une variété. C.R. Acad. Sci. Paris230, 508 (1950)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.