most recent 30 from http://mathoverflow.net 2013-05-21T09:18:26Z http://mathoverflow.net/feeds/question/47466 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/47466/how-do-i-compute-the-compact-cohomology-of-a-hypersurface Eric Zaslow 2010-11-26T21:48:20Z 2010-11-27T23:18:52Z

<p>How do I compute the compact cohomology of a hypersurface? For example, let $f$ be a Newton polynomial of a polytope in $\mathbb{R}^n$ and let $X = (f=0)$ inside $(\mathbb{C}^*)^n$ (maybe there is some dependency on the coefficients of $f\;$?). Can you tell me anything about $H^*_c(X)$? Perhaps I should know better, but I don't. Thanks!</p>

http://mathoverflow.net/questions/47466/how-do-i-compute-the-compact-cohomology-of-a-hypersurface/47493#47493 Balazs 2010-11-27T09:08:25Z 2010-11-27T09:08:25Z

<p>The classic reference is Danilov-Khovanskii's "Newton polyhedra and an algorithm for calculating Hodge-Deligne numbers". There is subsequent work by Cox, Batyrev, Malvyutov, etc. but they are mainly concerned with more general toric ambient spaces; if you want a hypersurface in the torus then this original paper should have all you need. </p>