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2 results

  • On the algebraicity of the zero locus of an admissible normal function

  • Part of
  • Patrick Brosnan, Gregory Pearlstein
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 11 / November 2013
    Published online by Cambridge University Press:
    28 August 2013, pp. 1913-1962
    Print publication:
    November 2013
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  • We show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic. In Part II of the paper, which is an appendix, we compute the Tannakian Galois group of the category of one-variable admissible real nilpotent orbits with split limit. We then use the answer to recover an unpublished theorem of Deligne, which characterizes the ${\mathrm{sl} }_{2} $-splitting of a real mixed Hodge structure.

  • On Strongly Normal Functions

  • Huaihui Chen, Paul M. Gauthier
  • Journal:
    Canadian Mathematical Bulletin / Volume 39 / Issue 4 / 01 December 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 408-419
    Print publication:
    01 December 1996
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  • Loosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.