The involutive structure on the blow-up of R^n in C^n

Details The involutive structure on the blow-up of R^n in C^n The involutive structure on the blow-up of R^n in C^n

1996-11-07

arxiv.org/abs/math/9611201v1

Mathematics

Complex Variables

Scientific paper

We investigate the natural involutive structure on the blow-up of ${\Bbb R}^n$ in ${\Bbb C}^n$ extending the complex structure on the complement of the exceptional hypersurface. Our main result is that this structure is hypocomplex, meaning that any solution is locally a holomorphic function of a basic set of independent solutions. We show this by an elementary power series argument but note that the result is essentially equivalent to the Edge of the Wedge Theorem. In particular, we obtain a relatively simple new proof of this classical theorem.

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