Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2012

    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?

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJan 4th 2012
    • (edited Jan 4th 2012)

    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.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeJan 4th 2012
    • (edited Jan 4th 2012)

    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.