most recent 30 from http://mathoverflow.net 2013-05-23T16:27:38Z http://mathoverflow.net/feeds/question/17146 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17146/positivity-properties-of-virtual-hodge-numbers-of-calabi-yaus Allen Knutson 2010-03-04T23:46:08Z 2010-03-04T23:46:08Z

<p>Let $X$ be a normal, projective complex variety with an anticanonical divisor $D$. Do the virtual Hodge numbers of the noncompact Calabi-Yau variety $X$ \ $D$ enjoy some sort of positivity property? </p> <p>Being virtual, defined by inclusion-exclusion from complete varieties, they're not individually positive. What I'd most like is to hear "The Euler characteristic is nonnegative". But that's not true for $X$ a quintic 3-fold, $D$ empty. </p>