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A curve of genus $2$ over ℂ(t) and hexads of bitangents to a smooth quartic
Abstract
In this paper we study the Abel-Jacobi map of a genus 2 curve over ℂ(t) arising from a double cover of ℙ2(ℂ) branched along six lines. We utilize the so-called Mumford representations to conduct the calculations. As an application, we give an alternative proof of classical results on quartics and bitangents. Furthermore, we obtain a method to give explicit defining equations of quartic curves that have the six lines as bitangents and apply it to determine the number of connected components of the realization space.
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BibTeX
@misc{bannai2026curve,
title = {{A curve of genus $2$ over $\mathbbC(t)$ and hexads of bitangents to a smooth quartic}},
author = {Shinzo Bannai and Hiro-o Tokunaga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38071},
eprint = {2610.38071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38071},
}
RIS
TY - UNPB
TI - A curve of genus $2$ over ℂ(t) and hexads of bitangents to a smooth quartic
AU - Shinzo Bannai
AU - Hiro-o Tokunaga
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.38071
UR - https://arxiv.org/abs/2610.38071
AB - In this paper we study the Abel-Jacobi map of a genus 2 curve over ℂ(t) arising from a double cover of ℙ^2(ℂ) branched along six lines. We utilize the so-called Mumford representations to conduct the calculations. As an application, we give an alternative proof of classical results on quartics and bitangents. Furthermore, we obtain a method to give explicit defining equations of quartic curves that have the six lines as bitangents and apply it to determine the number of connected components of the realization space.
ER -