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PreprintCC0arXiv

Degree of irrationality of a product of two elliptic curves

  • Yongnam Lee
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Abstract

In this short paper, we prove that, for any two complex elliptic curves E and F, the product E× F has degree of irrationality 3. The upper bound is obtained from compatible cyclic plane-cubic models of E and F: three diagonal bihomogeneous sections define a dominant rational map E× Fdashrightarrowℙ2 of degree 3. The lower bound follows by excluding dominant rational maps of degrees 1 and 2 from an abelian surface to ℙ2.

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Cite

BibTeXRIS
BibTeX
@misc{lee2026degree,
  title = {{Degree of irrationality of a product of two elliptic curves}},
  author = {Yongnam Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.22178},
  eprint = {2608.22178},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22178},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Degree of irrationality of a product of two elliptic curves
AU  - Yongnam Lee
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.22178
UR  - https://arxiv.org/abs/2608.22178
AB  - In this short paper, we prove that, for any two complex elliptic curves E and F, the product E× F has degree of irrationality 3. The upper bound is obtained from compatible cyclic plane-cubic models of E and F: three diagonal bihomogeneous sections define a dominant rational map E× Fdashrightarrowℙ^2 of degree 3. The lower bound follows by excluding dominant rational maps of degrees 1 and 2 from an abelian surface to ℙ^2.
ER  -