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Schottky Uniformization of Real Algebraic Curves and an Application to Moduli
Author(s) -
Huisman Johannes
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200105)225:1<75::aid-mana75>3.0.co;2-l
Subject(s) - mathematics , algebraic curve , invertible matrix , schottky diode , pure mathematics , algebraic number , moduli of algebraic curves , group (periodic table) , moduli space , algebra over a field , mathematical analysis , physics , optoelectronics , diode , chemistry , organic chemistry
We show that a nonsingular compact connected real algebraic curve can be uniformized by a real Schottky group, i. e., a Schottky group in PGL 2 (ℂ) which is actually contained in PGL 2 (ℝ). As an application we show that the set M rp g /ℝ of isomorphismclasses of nonsingularcompact connected real algebraic curves of genus g having real points, has a structure of a semianalytic variety. We show that this structure coincides with the semianalytic structure on M rp g /ℝ defined via real Teichmüller spaces.