NOETHER INEQUALITY FOR A NEF AND BIG DIVISOR ON A SURFACE Shin, Dong-Kwan;
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.
linear system;Noether inequality;nef and big divisor;
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