极化阿贝尔曲面的合冲：Reider型准则
Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion
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中文总结 AI 辅助
本文针对极化阿贝尔曲面建立了关于性质$N_p$的Reider型准则，给出了$d$的最优数值界，改进了前人工作，还构造了基点自由阈值为无理数的极化阿贝尔曲面。
中文摘要 AI 辅助
设$(X,L)$为满足$L^2=2d$的极化复阿贝尔曲面，本文建立了关于性质$N_p$的Reider型准则。若$d\geq7$，则$L$满足性质$N_0$当且仅当$X$中不存在椭圆曲线$E$使得$L\cdot E\leq2$，存在一个明确描述的例外情况；若$p\geq1$且$d\geq(p+2)^2+1$，则$L$满足性质$N_p$当且仅当$X$中不存在椭圆曲线$E$使得$L\cdot E\leq p+2$。$d$的数值界对$p=0,1$是最优的，这些结果改进了Küronya--Lozovanu、Ito及Rojas的早期工作，本文还构造了一个基点自由阈值为无理数的极化阿贝尔曲面。
英文摘要
Let $(X,L)$ be a polarized complex abelian surface with $L^2=2d$. We establish a Reider-type criterion for Property $N_p$. If $d\geq7$, then $L$ satisfies Property $N_0$ if and only if there is no elliptic curve $E\subseteq X$ with $L\cdot E\leq2$, with one explicitly described exception. If $p\geq1$ and $d\geq(p+2)^2+1$, then $L$ satisfies Property $N_p$ if and only if there is no elliptic curve $E\subseteq X$ with $L\cdot E\leq p+2$. The numerical bounds on $d$ are optimal for $p=0,1$. These results improve upon earlier work of Küronya--Lozovanu, Ito, and Rojas. We also construct a polarized abelian surface whose basepoint-freeness threshold is irrational.
