Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 245-258

ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES

Gabriel Bartolini, Antonio F. Costa and Milagros Izquierdo

Linköpings Universitet, Matematiska Institutionen
581 83 Linköping, Sweden; gabriel.bartolini 'at' liu.se

UNED, Facultad de Ciencias, Departamento de Matemáticas Fundamentales
28040 Madrid, Spain; acosta 'at' mat.uned.es

Linköpings Universitet, Matematiska Institutionen
581 83 Linköping, Sweden; milagros.izquierdo 'at' liu.se

Abstract. The moduli space M_g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B_g. In this article we show that B_g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

2010 Mathematics Subject Classification: Primary 14h15, 30F10, 32G15.

Key words: Branch locus, moduli space, equisymmetric stratification, automorphisms of Riemann surfaces.

Reference to this article: G. Bartolini, A.F. Costa and M. Izquierdo: On the connectivity of branch loci of moduli spaces. Ann. Acad. Sci. Fenn. Math. 38 (2013), 245-258.

Full document as PDF file

doi:10.5186/aasfm.2013.3820

Copyright © 2013 by Academia Scientiarum Fennica