A lower bound for K_XL of quasi-polarized surfaces (X,L) with non-negative Kodaira dimension

1996/07/15 by Fukuma, Yoshiaki
#14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9607013

Abstract

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 κ(X)≥ 0, then K_XL≥ 2q(X)-4, where q(X) is the irregularity of X. In this paper, we prove that this conjecture is true if (1) the case in which κ(X)=0 or 1, (2) the case in which κ(X)=2 and h⁰(L)≥ 2, or (3) the case in which κ(X)=2, X is minimal, h⁰(L)=1, and L satisfies some conditions.

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