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Morrison, D. R.

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

Invent. Math. 75, 105-121 (1984).
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Cited in 5 Reviews
Cited in 122 Documents

MSC:

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

Keywords:

large Picard number; Neron-Severi group; K3 surface; Shioda-Inose structure; Kummer surface; Hodge structure; intersection forms; Oda conjecture

Citations:

Zbl 0374.14006; Zbl 0459.14003; Zbl 0454.14017; Zbl 0433.14024; Zbl 0312.14008; Zbl 0325.14015; Zbl 0427.10014; Zbl 0408.10011
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\textit{D. R. Morrison}, Invent. Math. 75, 105--121 (1984; Zbl 0509.14034)
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References:

[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)
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