One dimensional equisymmetric strata in moduli space
| Autor: | S. Broughton, Antonio Costa, Milagros Izquierdo |
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| Rok vydání: | 2022 |
| Zdroj: | Contemporary Mathematics. :177-215 |
| ISSN: | 1098-3627 0271-4132 |
| Popis: | The moduli space M g \mathcal {M}_{g} of surfaces of genus g ≥ 2 g\geq 2 is the space of conformal equivalence classes of closed Riemann surfaces of genus g g . This space is a complex, quasi-projective variety of dimension 3 g − 3 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 stratified 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. |
| Databáze: | OpenAIRE |
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