## Journal of Mathematics of Kyoto University

### On splitting of certain Jacobian varieties

Ryo Nakajima

#### Abstract

We give three examples of non-hyperelliptic curves of genus 4 whose Jacobian varieties are isomorphic to products of four elliptic curves. Two of the examples belong to one-parameter families of curves whose Jacobian varieties are isomorphic to products of two 2-dimensional complex tori. By constructing analogous families, we prove that for each $n>1$, there is a one-parameter family of non-hyperelliptic curves of genus $2n$ whose Jacobian varieties are isomorphic to products of two $n$-dimensional tori.

#### Article information

Source
J. Math. Kyoto Univ., Volume 47, Number 2 (2007), 391-415.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281052

Digital Object Identifier
doi:10.1215/kjm/1250281052

Mathematical Reviews number (MathSciNet)
MR2376963

Zentralblatt MATH identifier
1144.14024

Subjects