Complex projective structures

  • David Dumas

    University of Illinois at Chicago, USA
Complex projective structures cover

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This is a survey of the theory of complex projective ℂℙ1-structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics:

  1. Using the Schwarzian derivative to parameterize the moduli space
  2. Thurston’s parameterization of the moduli space using grafting
  3. Holonomy representations of ℂℙ1-structures

We also discuss some results comparing the two parameterizations of the space of projective structures and relating these parameterizations to the holonomy map.