Title

7-Gons and genus three hyperelliptic curves

Document Type

Article

Publication Date

3-1-2013

Abstract

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(ζ7 + ζ̄7). We study the algebraic correspondences on these curves which are lifts of algebraic correspondences on a conic in P2 associated with Poncelet 7-gons. These correspondences induce endomorphisms φ on the Jacobians which satisfy φ3+φ2-2φ-1=0. Moreover, we study Humbert's modular equations which characterize the curves of genus three having these real multiplications. © 2012 Springer-Verlag.

Publication Source (Journal or Book title)

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

First Page

35

Last Page

52

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