STRONG q-CONVEXITY IN UNIFORM NEIGHBORHOODS OF SUBVARIETIES IN COVERINGS OF COMPLEX SPACES

نویسنده

  • MICHAEL FRABONI
چکیده

The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X , there is a neighborhood Ω of Y such that, for any covering space Υ: X̂ → X in which Ŷ ≡ Υ(Y ) has no noncompact connected analytic subsets of pure dimension q with only compact irreducible components, there exists a C∞ exhaustion function φ on X̂ which is strongly q-convex on Ω̂ = Υ(Ω) outside a uniform neighborhood of the q-dimensional compact irreducible components of Ŷ .

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تاریخ انتشار 2008