VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Tame sets in the complement of algebraic variety
    Kolarič, Dejan
    Let ▫$A \subset {\mathbb C}^N$▫ be an algebraic variety with ▫$\dim A \le N-2$▫. Given discrete sequences ▫$\{a_j\}, \{b_j\} \subset {\mathbb C}^N \setminus A$▫ with slow growth ▫$(\sum_j ... \frac{1}{|a_j|^2} \le \infty, \sum_j \frac{1}{|b_j|^2} \le \infty)$▫ we construct a holomorphic automorphism ▫$F$▫ with ▫$F(z)=z$▫ for all ▫$z \in A$▫ and ▫$F(a_j)=b_j$▫ for all ▫$j \in {\mathbb N}$▫. Additional approximation of a given automorphism on a compact polynomially convex set, fixing ▫$A$▫, is also possible. Given unbounded analytic variety ▫$A$▫ there is a tame set ▫$E$▫ such that ▫$F(E) \ne \{(j,0^{N-1}):j \in {\mathbb N}\}$▫ for all automorphisms ▫$F$▫ with ▫$F|_A = id$▫. As an application we obtain an embedding of a Stein manifold into the complement of an algebraic variety in ▫${\mathbb C}^N$▫ with interpolation on a given discrete set.
    Vir: The Journal of geometric analysis. - ISSN 1050-6926 (Vol. 19, no. 4, 2009, str. 847-863)
    Vrsta gradiva - članek, sestavni del
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 15194713

    Povezava(-e):

    http://dx.doi.org/10.1007/s12220-009-9089-4
    DOI

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