Abstract
We study the relations between Poncelet 5-gons, abelian surfaces with real multiplication and the Hilbert modular surfaceY(5) for the number field\(\mathbb{Q}\left( {\sqrt 5 } \right)\). These objects are linked by the construction of Kummer surfaces as double convers of the projective plane. Constructing a map from the moduli space of Poncelet 5-gons toY(5), we get a new proof for the rationality ofY(5). As a corollary we get a theorem of plane projective geometry (due to Humbert) describing the combinatorial symmetries of Poncelet pairs of conics with a Poncelet 5-gon and a bitangent.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
