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currently the bulk of the entry analytic geometry is occupied by a long section on “Holomorphic functions of several complex variables”. Should that not better be moved to some dedicated entry of its own? Any opinions?
This is the mainstream analytic geometry. I mean Hartogs theorem, domains of holomorphy, pseudoconvexity, this is abc of analytic geometry. Rigid analytic geometry should also be represented (again, not only in Berkovich approach) but it is more esoteric subject and it has entry rigid analytic geometry. Book of Jean Dieudonné Panorama of pure mathematics is having a famous chapter on analytic geometry which surveys it in a similar way. Area of several complex varaibles has its aspects which are more geometric and belong to analytic geometry but it also has functional aspects dealing with analytic PDEs, potential theory, functional spaces on complex manifolds etc. Thus it is not good to delegate the geometric aspects too much to several complex variables.
I should also point out that analytic space in complex geometry is a wide generalization of a complex analytic manifold, and it has been developed in French and German schools in 1950s and 1960s – Henri Cartan, Grauert, Remmert etc. and the books by Grauert and Remmert are quite a good account. I will make some changes to analytic space to reflect this. I mean one has to include all variants, archimedean and non-archimedean.
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