Degree of irrationality of a product of two elliptic curves

Yoshihara, Hisao

doi:10.1090/S0002-9939-96-03375-8

Degree of irrationality of a product of two elliptic curves
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Proc. Amer. Math. Soc. 124 (1996), 1371-1375 Request permission

Abstract:

We consider the degree of irrationality $d_r(S)$ of some algebraic surface $S$. Firstly we give an estimate of $d_r(S)$ for a surface $S$ with a structure of a fiber space. Secondly we prove the existence of a nonsingular curve of genus 3 on $E\times E$ for a certain elliptic curve $E$ with complex multiplications. As a corollary, we obtain that $d_r(E\times E)=3$.

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