complex analytic space
Could not include synthetic complex geometry - contents
The notion of complex analytic space is the notion of analytic space in complex geometry; the generalization of the notion of complex manifold to spaces with singularities.
A complex analytic test space is a common vanishing locus of a set of holomorphic functions . This is naturally a locally ringed space over the complex numbers . A complex analytic space is a locally ringed space over that is locally isomorphic to such a complex analytic test space.
A smooth complex analytic space is locally isomorphic to a polydisc and hence locally contractible. See also (Berkovich, p.2).
- Brian Osserman, Complex varieties and the analytic topology (pdf)
Generalization of smooth complex analytic spaces to smooth -adic analytic spaces is discussed in
Revised on December 20, 2012 04:15:25
by Urs Schreiber