intersection cohomology when the resolution is not semi-small - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:35:31Z http://mathoverflow.net/feeds/question/8935 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/8935/intersection-cohomology-when-the-resolution-is-not-semi-small intersection cohomology when the resolution is not semi-small Vinoth 2009-12-15T01:36:21Z 2009-12-15T07:58:39Z <p>When we have a variety and a resolution of singularities, but it is not semi-small (i.e. the dimensions of the fibres do not satisfy the right conditions), then what can we say about the intersection cohomology? Someone was telling me something about this with shifting the IC or something, but I cannot remember the precise statement. </p> http://mathoverflow.net/questions/8935/intersection-cohomology-when-the-resolution-is-not-semi-small/8968#8968 Answer by Mike Skirvin for intersection cohomology when the resolution is not semi-small Mike Skirvin 2009-12-15T07:58:39Z 2009-12-15T07:58:39Z <p>I'm not sure exactly what question you're asking. I think you may be looking for the following answer. By the decomposition theorem, the intersection cohomology of the variety is a direct summand of the cohomology of the resolution. I'm not sure there's anything more specific you can say than that in general.</p>