幾何セミナー


2018/8/6(Mon)

13:00--14:30

千葉優作

お茶の水女子大学

Cohomology of non-pluriharmonic loci

Pseudoconvex domains play an important role in complex analysis. It is known that the de Rham cohomology of a pseudoconvex domain is 0 if the degree is larger than the dimension of the domain. In this talk, we study the low degree cohomology of a pseudoconvex domain. We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function. This result may be regarded as a pseudoconvex counterpart of the Lefschetz hyperplane theorem.