INTEGRATION OF A DIFFERENTIAL FORM ON AN ANALYTIC COMPLEX SUBVARIETY | Zendy

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INTEGRATION OF A DIFFERENTIAL FORM ON AN ANALYTIC COMPLEX SUBVARIETY

Author(s) -

Pierre Lelong

Publication year - 1957

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.43.2.246

Subject(s) - induced pluripotent stem cell , neuroscience , stem cell , myocyte , cardiac electrophysiology , microbiology and biotechnology , cell , electrophysiology , in vitro , biology , computational biology , biomedical engineering , medicine , biochemistry , embryonic stem cell , gene

for an exterior differential form so on an analytic complex subvariety W. The problem arises because an analytic complex subvariety in a domain D of Cn (or, more briefly, an analytic set in D) is not, in general, a manifold. We give (a) an existence theorem for t(p) and (b) a proof that t is a closed current in D, that is, t(4b) = 0 for the forms 41 with compact support, which are homologous to zero in D. II. A set W is called an analytic set in a domain D of Cn(zl, ..., zn) if M e D has a neighborhood (UM) such that (UM) n W is defined by the simultaneous equations

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