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.

Metadaten
Author:	Jan-Christoph Schlage-Puchta, Jürgen Wolfart GND
URN:	urn:nbn:de:hebis:30-11860
URL:	http://www.math.uni-frankfurt.de/~wolfart/wolfart.html
Document Type:	Preprint
Language:	English
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
Note:	Preprint, Frankfurt a.M. 2004, erscheint im Archiv d. Math.
Source:	http://www.math.uni-frankfurt.de/~wolfart/wolfart.html, Preprint, Frankfurt a.M. 2004, erscheint im Archiv d. Math.
HeBIS-PPN:	129536733
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):	Deutsches Urheberrecht

Open Access