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Möbius automorphisms of surfaces with many circles

Part of: Nonlinear incidence geometry Cycles and subschemes Analytic and descriptive geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  02 September 2020

Niels Lubbes
Niels Lubbes*
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Vienna, Austria
*
e-mail: niels.lubbes@gmail.com
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Abstract

We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a Möbius automorphism group of dimension at least two. Our theorem generalizes the classical classification of Dupin cyclides.

Keywords

Surface automorphismsweak del Pezzo surfacesMöbius geometrycirclesLie algebrastoric geometrylattice geometry

MSC classification

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 51B10: Möbius geometries 51N30: Geometry of classical groups 14C20: Divisors, linear systems, invertible sheaves

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 1 , February 2022 , pp. 42 - 71
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Copyright
© Canadian Mathematical Society 2020

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