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NOETHER INEQUALITY FOR A NEF AND BIG DIVISOR ON A SURFACE
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 Title & Authors
NOETHER INEQUALITY FOR A NEF AND BIG DIVISOR ON A SURFACE
Shin, Dong-Kwan;
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 Abstract
For a nef and big divisor D on a smooth projective surface S, the inequality (S;) is well known. For a nef and big canonical divisor KS, there is a better inequality (S;) which is called the Noether inequality. We investigate an inequality (S;) like Clifford theorem in the case of a curve. We show that this inequality holds except some cases. We show the existence of a counter example for this inequality. We prove also the base-locus freeness of the linear system in the exceptional cases.
 Keywords
linear system;Noether inequality;nef and big divisor;
 Language
English
 Cited by
 References
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W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Springer-Verlag, Berlin-Heidelberg-New-York, 1984

2.
P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New-York, 1978

3.
M. Kobayashi, On Noether's inequality for threefolds, J. Math. Soc. Japan 44 (1992), no. 1, 145-156 crossref(new window)

4.
B. Saint-Donat, Projective models of K3 surfaces, Amer. J. of Math. 96 (1974), no. 4, 602-639 crossref(new window)