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    • A geometric characterization of arithmetic varieties

      Kapil Hari Paranjape

      Volume 112 Issue 3 August 2002 pp 383-391

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/112/03/0383-0391

    • Keywords

       

      Equisingular; geometrically rigid

    • Abstract

       

      A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.

    • Author Affiliations

       

      Kapil Hari Paranjape1

      1. Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai - 600 113, India

    • Dates

       
      Published
      August 2002
      Manuscript received
      8 November 2001
      Manuscript revised
      2 May 2002

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