The Prym-Green conjecture in even genera up to 30

Sam Payne; Thomas Willwacher

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arXiv · 2610.05646

The Prym-Green conjecture in even genera up to 30

Sam Payne·Thomas Willwacher

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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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Sam Payne, Thomas Willwacher. 2026-10-05. The Prym-Green conjecture in even genera up to 30. https://arxiv.org/abs/2610.05646

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