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Classification of algebraic non-ruled surfaces with sectional genus less than or equal to six

Published online by Cambridge University Press:  22 January 2016

Elvira Laura Livorni*
Affiliation:
Istituto di Matematica Universita’ Degli Studi Dell’ Aquila Degli Abruzzi, via Roma, 33, 67100 L’AQUILA, Italy
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In this paper we have given a biholomorphic classification of smooth, connected, protective, non-ruled surfaces X with a smooth, connected, hyperplane section C relative to L, where L is a very ample line bundle on X, such that g = g(C) = g(L) is less than or equal to six. For a similar classification of rational surfaces with the same conditions see [Li].

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[Bo+Hu] Bombieri, E. and Husemoller, D., Classification and embeddings of surfaces, Proc. of Symposia in Pure Math., 29 (1975), 329420.Google Scholar
[G+H4] Griffiths, P. A. and Harris, J., Principles of Algebraic Geometry, A. Wiley-Inter science publication, (1978).Google Scholar
[Ha] Hartshorne, R., Algebraic Geometry, Springer-Verlag, New York, (1977).Google Scholar
[Ho+Mu] Horrocks, G. and Mumford, D., Topology, Pergman Press, 12 (1973), 6381.Google Scholar
[Io] Ionescu, P., An enumeration of all smooth protective varieties of degree 5 and 6, Preprint Series in Mathematics NR 74/1981.Google Scholar
[Li] Livorni, E. L., Classification of Algebraic surfaces with sectional genus less than or equal to six, I: Rational Surfaces, J. Pacific Math. Vol. 113, No. I, 1984, 93114.Google Scholar
[Na] Nagata, M., On rational surfaces I, Mem. Coll. Sci. Kyoto (A) 32 (1960), 351370.Google Scholar
[Ro] Roth, L., On the protective classification of surfaces, Proc. London Math. Soc. 2nd series, 42 (1937), 142170.Google Scholar
[Sa1] B. Saint, Donat, Protective models of K-3 surfaces. J. Amer., of Math., 96 (1972), 602639.Google Scholar
[Sa2] Saint-Donat, B., On Petri’s analysis of the linear system of quadrics through a canonical curve, Math. Ann., 206 (1973), 157175.Google Scholar
[So] Sommese, A. J., Hyperplane sections of projective surfaces I—The adjunction mapping, Duke Math. J., 46 (1979) No. 2.Google Scholar