How many quasiplatonic surfaces?

  • We show that the number of isomorphism classes of quasiplatonic Riemann surfaces of genus <= g has o growth of typ g exp (log g). The number of non-isomorphic regular dessins of genus <= g has the same growth type.

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Author:Jan-Christoph Schlage-Puchta, Jürgen WolfartGND
Document Type:Preprint
Date of Publication (online):2005/06/29
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/29
Tag:Dessins d'enfants; compact Riemann surfaces; subgroup growth
Preprint, Frankfurt a.M. 2004, erscheint im Archiv d. Math.
Source:, Preprint, Frankfurt a.M. 2004, erscheint im Archiv d. Math.
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:14-XX ALGEBRAIC GEOMETRY / 14Hxx Curves / 14H30 Coverings, fundamental group [See also 14E20, 14F35]
20-XX GROUP THEORY AND GENERALIZATIONS / 20Exx Structure and classification of infinite or finite groups / 20E07 Subgroup theorems; subgroup growth
30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Fxx Riemann surfaces / 30F10 Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
Licence (German):License LogoDeutsches Urheberrecht