PreprintCC BY 4.0arXiv
Non-algebraicity of the Lawson surfaces ξk,l
Abstract
We prove that every Lawson surface ξk,l⊂𝕊3 of genus kl>1 is non-algebraic: any real polynomial vanishing on ξk,l vanishes identically on 𝕊3. This answers a question posed by Hsiang in 1967 and proves Lawson's 1970 conjecture for ξ2,2. The proof uses a reflection principle for the monodromy of the associated family of flat connections.
Related
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- A Secondary Multiplicative Structure on Lawson Homology
BibTeX
@misc{heller2026nonalgebraicity,
title = {{Non-algebraicity of the Lawson surfaces $ξ_k,l$}},
author = {Lynn Heller and Sebastian Heller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16853},
eprint = {2610.16853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16853},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-algebraicity of the Lawson surfaces ξ_k,l
AU - Lynn Heller
AU - Sebastian Heller
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.16853
UR - https://arxiv.org/abs/2610.16853
AB - We prove that every Lawson surface ξ_k,l⊂𝕊^3 of genus kl>1 is non-algebraic: any real polynomial vanishing on ξ_k,l vanishes identically on 𝕊^3. This answers a question posed by Hsiang in 1967 and proves Lawson's 1970 conjecture for ξ_2,2. The proof uses a reflection principle for the monodromy of the associated family of flat connections.
ER -