the Cech-cohomology of the sheaf of germs of plurisubharmonic functions defined on a domain in C^n - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T15:54:51Z http://mathoverflow.net/feeds/question/17345 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17345/the-cech-cohomology-of-the-sheaf-of-germs-of-plurisubharmonic-functions-defined-o the Cech-cohomology of the sheaf of germs of plurisubharmonic functions defined on a domain in C^n HKSHLZW 2010-03-07T01:56:21Z 2010-03-07T02:28:27Z <p>we all know that if we consider the sheaf of germs of a holomorphic functions defined on a domain in C^n,we have too many beautiful theorems characterizing the geometry of the domain by consider the Cech-cohomology of the sheaf.Then i think that plurisubharmonic functions is in some sense a weaker function than holomorphic functions.So we may get some beautiful theorems as the case of holomorphic case, for example if we can proof that for a domain in C^n,the first Cech-cohomology of the sheaf of germs of plurisubharmonic functions vanishes ,we then can choose any good plurisubharmonic functions as we want. What i want to ask is that have you ever considered such a question ,and i don't know whether this is a good question ? I want to hear some suggestions.</p> http://mathoverflow.net/questions/17345/the-cech-cohomology-of-the-sheaf-of-germs-of-plurisubharmonic-functions-defined-o/17350#17350 Answer by algori for the Cech-cohomology of the sheaf of germs of plurisubharmonic functions defined on a domain in C^n algori 2010-03-07T02:28:27Z 2010-03-07T02:28:27Z <p>As Petya has pointed out, plurisubharmonic functions on an open set do not form a group, so when one sheafifies, one gets a sheaf of sets, not groups; it has H^0, but no higher cohomology.</p>