Publicación: Modular companions in planar one-dimensional equisymmetric strata
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2025
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info:eu-repo/semantics/openAccess
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Universal Wiser
Este artículo será publicado próximamente. This article will be published soon.
Este artículo será publicado próximamente. This article will be published soon.
Resumen
Consider, in the moduli space of Riemann surfaces of a fixed genus, the subset of surfaces with non-trivial automorphisms. Of special interest are the numerous subsets of surfaces admitting an action of a given finite group, G, acting with a specific signature. In a previous study [6], we declared two Riemann surfaces to be modular companions if they have topologically equivalent G actions, and that their G quotients are conformally equivalent orbifolds. In this article we present a geometrically-inspired measure to decide whether two modular companions are conformally equivalent (or how different), respecting the G action. Along the way, we construct a moduli space for surfaces with the specified G action and associated equivariant tilings on these surfaces.
We specifically apply the ideas to planar, finite group actions whose quotient orbifold is a sphere with four cone points
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Centro
Facultades y escuelas::Facultad de Ciencias
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Matemáticas Fundamentales