偶数亏格至30的Prym-Green猜想
The Prym-Green conjecture in even genera up to 30
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中文总结 AI 辅助
本文证明了20至30所有偶数亏格的Prym-Green猜想，并利用有理结点曲线与块Wiedemann算法完成证明。
中文摘要 AI 辅助
我们证明了从20到30的所有偶数亏格的Prym-Green猜想。亏格24的情形反驳了Chiodo-Eisenbud-Farkas-Schreyer提出的该猜想可能在每个被8整除的亏格中失败的猜测。我们的证明利用具有循环对称性的有理结点曲线，将相关的Koszul微分分解为按字符索引的较小映射的直和。我们使用块Wiedemann算法在有限域上执行所得的秩计算。
英文摘要
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.
