Article
One dimensional equisymmetric strata in moduli space
Contemporary Mathematics, accepted
(2021)
Abstract
The moduli space Mg of surfaces of genus g >1 is the space of
conformal equivalence classes of closed Riemann surfaces of genus g. This space
is a complex, quasi-projective variety of dimension 3g-3. The singularity set
of the moduli space, which is roughly the same as the branch locus, becomes
increasingly complicated as the genus grows. To better understand the branch
locus, the moduli space may be stratifi ed into a finite, disjoint union of smooth,
irreducible, quasi-projective subvarieties called equisymmetric strata. Each
stratum corresponds to a collection of surfaces of the same symmetry type.
The topology of these strata is largely unknown. In this paper we explore
the topology of the complex 1-dimensional strata, which are smooth,
connected, complex curves with punctures. We are able to describe the topology
of these strata explicitly, as punctured Riemann surfaces, in terms of the
action of the automorphism group of the surfaces in the stratum.
Keywords
- automorphism of Riemann surface,
- moduli space,
- branch locus,
- equisymmetry
Disciplines
Publication Date
April 27, 2021
Citation Information
Sean A Broughton, Antonio F. Costa and Milagros Izquierdo. "One dimensional equisymmetric strata in moduli space" Contemporary Mathematics, accepted (2021) Available at: http://works.bepress.com/allen_broughton/99/