PreprintCC BY 4.0arXiv
Degree of irrationality of abelian surfaces
Abstract
Let A be a complex abelian surface. We prove that A admits a dominant rational map of degree three to PP2 if and only if it admits a polarization of type (1,1), (1,2), (1,3), or (1,6). Consequently, the degree of irrationality of A is $3$ precisely in these four cases and is $4$ otherwise.
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BibTeX
@misc{huang2026degree,
title = {{Degree of irrationality of abelian surfaces}},
author = {Songsong Huang and Zhi Jiang and Xin Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02169},
eprint = {2609.02169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02169},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Degree of irrationality of abelian surfaces
AU - Songsong Huang
AU - Zhi Jiang
AU - Xin Yang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02169
UR - https://arxiv.org/abs/2609.02169
AB - Let A be a complex abelian surface. We prove that A admits a dominant rational map of degree three to PP^2 if and only if it admits a polarization of type (1,1), (1,2), (1,3), or (1,6). Consequently, the degree of irrationality of A is $3$ precisely in these four cases and is $4$ otherwise.
ER -