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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Degree of irrationality of a product
of two elliptic curves


Author: Hisao Yoshihara
Journal: Proc. Amer. Math. Soc. 124 (1996), 1371-1375
MSC (1991): Primary 14J25; Secondary 14K99
MathSciNet review: 1327053
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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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Additional Information

Hisao Yoshihara
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, 950-21 Niigata, Japan
Email: yosihara@geb.ge.niigata-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03375-8
PII: S 0002-9939(96)03375-8
Keywords: Degree of irrationality, abelian surface, elliptic curve with complex multiplications
Received by editor(s): October 13, 1994
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1996 American Mathematical Society