A Lower Bound For KxL Of Quasi-Polarized Surfaces (X, L) With Non-Negative Kodaira Dimension

Fukuma, Yoshiaki

Canadian journal of mathematics, Tome 50 (1998) no. 6, pp. 1209-1235

Résumé

Let $X$ be a smooth projective surface over the complex number field and let $L$ be a nef-big divisor on $X$ . Here we consider the following conjecture; If the Kodaira dimension $\kappa (X)\ge 0$ , then ${{K}_{X}}L\,\ge \,2q(X)\,-\,4$ , where $q\left( X \right)$ is the irregularity of $X$ . In this paper, we prove that this conjecture is true if (1) the case in which $\kappa (X)=0$ or 1, (2) the case in which $\kappa (X)=2$ and ${{h}^{0}}(L)\,\ge \,2$ , or (3) the case in which $\kappa (X)=2$ , $X$ is minimal, ${{h}^{0}}(L)\,=\,1$ , and $L$ satisfies some conditions.

Détail

DOI : 10.4153/CJM-1998-059-x

Mots-clés : 14C20, Quasi-polarized surface, sectional genus

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