Pseudo Kobayashi hyperbolicity of subvarieties of general type on abelian varieties

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Abstract

<p>We prove that the Kobayashi pseudo distance of a closed subvariety ๐‘‹ of an abelian variety ๐ด is a true distance outside the special set Sp(๐‘‹) of ๐‘‹, where Sp(๐‘‹) is the union of all positive dimensional translated abelian subvarieties of ๐ด which are contained in ๐‘‹. More strongly, we prove that a closed subvariety ๐‘‹ of an abelian variety is taut modulo Sp(๐‘‹); Every sequence ๐‘“<sub>๐‘›</sub> : ๐”ป โ†’ ๐‘‹ of holomorphic mappings from the unit disc ๐”ป admits a subsequence which converges locally uniformly, unless the image ๐‘“<sub>๐‘›</sub>(๐พ) of a fixed compact set ๐พ of ๐”ป eventually gets arbitrarily close to Sp(๐‘‹) as ๐‘› gets larger. These generalize a classical theorem on algebraic degeneracy of entire curves in irregular varieties.</p>

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 71(1), 259-298, 2019

    The Mathematical Society of Japan

Codes

  • NII Article ID (NAID)
    130007557120
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • ISSN
    0025-5645
  • NDL Article ID
    029459914
  • NDL Call No.
    Z53-A209
  • Data Source
    NDL  J-STAGE 
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