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2025
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Universal Wiser
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Este artículo será publicado próximamente. This article will be published soon.
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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