How do I compute the compact cohomology of a hypersurface? - MathOverflow 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 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 Answer by Balazs for How do I compute the compact cohomology of a hypersurface? 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>