7-Gons and genus three hyperelliptic curves
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, ISSN: 1579-1505, Vol: 107, Issue: 1, Page: 35-52
2013
- 2Citations
- 4Usage
- 3Captures
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Metrics Details
- Citations2
- Citation Indexes2
- CrossRef1
- Usage4
- Abstract Views4
- Captures3
- Readers3
Article Description
In this paper, we will give a general but completely elementary description for hyperelliptic curves of genus three whose Jacobian varieties have endomorphisms by the real cyclotomic field ℚ(ζ + ζ̄). We study the algebraic correspondences on these curves which are lifts of algebraic correspondences on a conic in P associated with Poncelet 7-gons. These correspondences induce endomorphisms φ on the Jacobians which satisfy φ+φ-2φ-1=0. Moreover, we study Humbert's modular equations which characterize the curves of genus three having these real multiplications. © 2012 Springer-Verlag.
Bibliographic Details
https://digitalcommons.lsu.edu/mathematics_pubs/494; https://repository.lsu.edu/mathematics_pubs/494
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84874091194&origin=inward; http://dx.doi.org/10.1007/s13398-012-0079-1; http://link.springer.com/10.1007/s13398-012-0079-1; http://link.springer.com/content/pdf/10.1007/s13398-012-0079-1; http://link.springer.com/content/pdf/10.1007/s13398-012-0079-1.pdf; http://link.springer.com/article/10.1007/s13398-012-0079-1/fulltext.html; https://digitalcommons.lsu.edu/mathematics_pubs/494; https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=1493&context=mathematics_pubs; https://repository.lsu.edu/mathematics_pubs/494; https://repository.lsu.edu/cgi/viewcontent.cgi?article=1493&context=mathematics_pubs; https://dx.doi.org/10.1007/s13398-012-0079-1; https://link.springer.com/article/10.1007/s13398-012-0079-1
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