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The Prym-Green conjecture in even genera up to 30
Sam Payne, Thomas Willwacher
Source 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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