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2019•arXiv (Cornell University)Open access

A differential form approach to the genus of Open Riemann surfaces

Franco Vargas Pallete, Jesus Zapata Samanez

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Abstract

We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the minimal genus where $M$ can be holomorphically embedded.

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What this paper is about

We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the minimal genus where $M$ can be holomorphically embedded.

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Available abstract

We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the minimal genus where $M$ can be holomorphically embedded.

Key concepts: Riemann surface, Genus, Quotient, Open set, Mathematics, Pure mathematics, Surface (topology), Riemann–Hurwitz formula

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