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On degrees and genera of curves on smooth quartic surfaces in P3

Published online by Cambridge University Press:  22 January 2016

Shigefumi Mori
Shigefumi Mori*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Our result is motivated by the results [GP] of Gruson and Peskin on characterization of the pair of degree d and genus g of a non-singular curve in P3. In the last step, they construct the required curve C on a singular quartic surface when Here we consider curves on smooth quartic surfaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 96 , December 1984 , pp. 127 - 132
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[GP] Gruson, L. and Peskin, C., Genre des courbes algébrique de l’espace projectif (II), Ann. Sci. Ecole Norm. Sup., Paris, 4º série, t. 15 (1982), 401–418.Google Scholar
[K] Kodaira, K., On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), 751–798.CrossRefGoogle Scholar
[MM] Mori, S. and Mukai, S., The uniruledness of the moduli space of curves of genus 11, to appear in the proceedings of Japan France symposium on algebraic geometry, 1982.Google Scholar
[SD] Saint-Donat, B., Projective models of K-3 surfaces, Amer. J. Math., 96 (1974), 602–639.Google Scholar
[SI] Shioda, T. and Inose, H., On singular K3 surfaces, Complex analysis and algebraic geometry, Iwanami Shoten, Cambridge University Press, 1977, 119–136.Google Scholar