A connection between birational automorphisms of the plane and linear system of curves
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49552DOI: 10.1016/j.cam.2015.01.026
ISSN: 0377-0427
Publisher
Elsevier
Date
2015-08-01Bibliographic citation
Pérez Díaz, S. & Blasco, A. 2015, “A connection between birational automorphisms of the plane and linear systems of curves”, Journal of Computational and Applied Mathematics, vol. 283, pp. 91-105.
Keywords
Birationality
Automorphism
Linear Systems of Curves
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2015.01.026Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2015 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
In this paper, we prove that there exits a one-to-one correspondence between birational automorphisms of the plane and pairs of pencils of curves intersecting in a unique point. As a consequence, we show how to construct birational automorphisms of the plane of a certain degree d (fixed in advance) from some curves generating two linear systems of curves of degrees d and ed, where ed = d − 2 for d > 2, and ed = 1 otherwise. In addition, we also get the inverse of the birational automorphism constructed, and we show that its degree is obtained from the degree of the linear system of curves. As a special case, we show how these results can be stated to polynomial birational automorphisms of the plane.
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