×

Examples of algebraic curves with totally split Jacobian. (Exemples de courbes algébriques à jacobienne complètement décomposable.) (French) Zbl 0789.14026

The authors prove the following theorem: If \(g\) belongs to the set \(S=(1\),…,29, 31, 33, 37, 40, 41, 43, 45, 47, 49, 50, 53, 55, 57, 61, 65, 73, 82, 97, 109, 121, 129, 145, 163, 217, 257, 325, 433, 649, 1297) then there exists a curve of genus \(g\) whose Jacobian is isogenous to a product of elliptic curves. These curves are constructed either as modular curves or as coverings of curves of genus 2 or 3. The theorem includes all well known examples of algebraic curves with decomposable Jacobians and many new ones in addition.

MSC:

14H40 Jacobians, Prym varieties
PDFBibTeX XMLCite