PreprintCC BY 4.0arXiv
The Prym-Green conjecture in even genera up to 30
Abstract
We prove the Prym-Green conjecture in every even genus from 20 to 30. The genus 24 case disproves the suggestion of Chiodo-Eisenbud-Farkas-Schreyer that the conjecture might fail in every genus divisible by 8. Our proof uses rational nodal curves with cyclic symmetry to decompose the relevant Koszul differential into a direct sum of smaller maps indexed by characters. We carry out the resulting rank computations over finite fields using the block Wiedemann algorithm.
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BibTeX
@misc{payne2026prymgreen,
title = {{The Prym-Green conjecture in even genera up to 30}},
author = {Sam Payne and Thomas Willwacher},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05646},
eprint = {2610.05646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05646},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Prym-Green conjecture in even genera up to 30
AU - Sam Payne
AU - Thomas Willwacher
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05646
UR - https://arxiv.org/abs/2610.05646
AB - We prove the Prym-Green conjecture in every even genus from 20 to 30. The genus 24 case disproves the suggestion of Chiodo-Eisenbud-Farkas-Schreyer that the conjecture might fail in every genus divisible by 8. Our proof uses rational nodal curves with cyclic symmetry to decompose the relevant Koszul differential into a direct sum of smaller maps indexed by characters. We carry out the resulting rank computations over finite fields using the block Wiedemann algorithm.
ER -