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Rational maps as Schwarzian primitives

Abstract : We study necessary and sufficient conditions for a meromorphic quadratic differential with prescribed poles to be the Schwarzian derivative of a rational map. We give geometric interpretations of these conditions. We also study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case, the analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.
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https://hal.archives-ouvertes.fr/hal-01228525
Contributor : Yan Gao <>
Submitted on : Sunday, January 24, 2016 - 9:34:43 AM
Last modification on : Monday, March 9, 2020 - 6:15:55 PM
Document(s) archivé(s) le : Monday, April 25, 2016 - 10:10:38 AM

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  • HAL Id : hal-01228525, version 2
  • ARXIV : 1511.04246

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Guizhen Cui, Yan Gao, Lei Tan, Rugh Hans Henrik. Rational maps as Schwarzian primitives. 2016. ⟨hal-01228525v2⟩

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