Hyperbolic Groups and Non-Compact Real Algebraic Curves

Natanzon, Sergey and Pratoussevitch, Anna ORCID: 0000-0003-2248-6382 (2021) Hyperbolic Groups and Non-Compact Real Algebraic Curves. Transformation Groups, 26 (2). pp. 631-640.

Access the full-text of this item by clicking on the Open Access link.

Text
realpoints.pdf - Author Accepted Manuscript
Download (320kB) | Preview

Official URL: http://dx.doi.org/10.1007/s00031-021-09644-1

Abstract

In this paper we study the spaces of non-compact real algebraic curves, i.e. pairs $(P,\tau)$, where $P$ is a compact Riemann surface with a finite number of holes and punctures and $\tau:P\to P$ is an anti-holomorphic involution. We describe the uniformisation of non-compact real algebraic curves by Fuchsian groups. We construct the spaces of non-compact real algebraic curves and describe their connected components. We prove that any connected component is homeomorphic to a quotient of a finite-dimensional real vector space by a discrete group and determine the dimensions of these vector spaces.

Item Type:	Article
Additional Information:	9 pages, 5 figures
Uncontrolled Keywords:	math.AG, math.AG, math.DG, Primary 30F50, 30F35, Secondary 30F60
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	15 Mar 2021 08:32
Last Modified:	18 Jan 2023 22:56
DOI:	10.1007/s00031-021-09644-1
Open Access URL:	http://doi.org/10.1007/s00031-021-09644-1
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3117163