most recent 30 from http://mathoverflow.net 2013-06-18T05:14:20Z http://mathoverflow.net/feeds/question/52799 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52799/on-base-locus-of-canoncal-linear-system-on-surfaces Michael Zhang 2011-01-21T23:26:58Z 2011-01-21T23:37:14Z

<p>Let $S$ be a minimal surface of general type over $\mathbb{C}$ with $p_g=h^0(K_S)>1$. As a convention, we can write $|K_S|=|M|+F$ such that $F$ is the fixed part. We know that $K_SM \le K_S^2$. </p> <p>However, is there a lower bound of $K_SM$ given by $K_S^2$? For example, $K_SM \ge aK_S^2$, which means that $K_SF$ can not be too big.</p>