Open Access
Summer 2011 On the real nerve of the moduli space of complex algebraic curves of even genus
Grzegorz Gromadzki, Ewa Kozłowska-Walania
Illinois J. Math. 55(2): 479-494 (Summer 2011). DOI: 10.1215/ijm/1359762398

Abstract

The real locus in the moduli space of complex algebraic curves of given genus consists of curves having real forms, that is, Riemann surfaces admitting a symmetry (anticonformal involution). The real locus is covered by subsets, each formed by curves having a given topological type determined by the number of connected components and the separability type of the real models of the curves. In this paper, we study the structure of the nerve corresponding to this covering, called the real nerve of complex algebraic curves, for even genera. We find its geometrical and homological dimension, and we obtain some results concerning its global geometrical properties. In the proofs, we use the equivalent language of Riemann surfaces and their symmetries.

Citation

Download Citation

Grzegorz Gromadzki. Ewa Kozłowska-Walania. "On the real nerve of the moduli space of complex algebraic curves of even genus." Illinois J. Math. 55 (2) 479 - 494, Summer 2011. https://doi.org/10.1215/ijm/1359762398

Information

Published: Summer 2011
First available in Project Euclid: 1 February 2013

zbMATH: 1273.30030
MathSciNet: MR3020692
Digital Object Identifier: 10.1215/ijm/1359762398

Subjects:
Primary: 30F
Secondary: 14H

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign

Vol.55 • No. 2 • Summer 2011
Back to Top