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

Published online by Cambridge University Press:  20 November 2018

Yoshiaki Fukuma
Yoshiaki Fukuma*
Affiliation:
Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan, [email protected]
*
Current address: Department of Mathematics, College of Education, Naruto University of Education, Takashima, Naruto-cho, Naruto-shi 772-8502, Japan email: [email protected]
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Abstract

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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.

Keywords

14C20Quasi-polarized surfacesectional genus
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 6 , 01 December 1998 , pp. 1209 - 1235
Copyright
Copyright © Canadian Mathematical Society 1998

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