Birational involutions of the real projective plane

Authors :: Ivan Cheltsov
Frédéric Mangolte
Egor Yasinsky
Susanna Zimmermann
Zimmermann, Susanna
School of Mathematics - University of Edinburgh
University of Edinburgh
Institut de Mathématiques de Marseille (I2M)
Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Centre de Mathématiques Laurent Schwartz (CMLS)
École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire Angevin de Recherche en Mathématiques (LAREMA)
Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS)
Source :: HAL
Publication Year :: 2022
Abstract: We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which includes 4 different classes of involutions, we discover 12 different classes over the reals, and provide many examples when the fixed curve of an involution does not determine its conjugacy class in the real plane Cremona group.

Subjects :: Mathematics - Algebraic Geometry
14E07, 14E05, 14E30, 14J45, 14P99
FOS: Mathematics
[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Algebraic Geometry (math.AG)
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]

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