论文标题
最大neorem定理用于单数曲线
Max Noether Theorem for Singular Curves
论文作者
论文摘要
Max Noether的定理断言，如果$ω$是非遗传非透明射击曲线的双重捆，则自然形态$ \ text {sym}^nh^0（ω）\ to H^0（ω）\ to H^0（ω^n）$是所有$ n \ geq geq eq f surmentive。许多不同的作者以不同的方式扩展了Gorenstein曲线的结果。最近，它证明了这种曲线的曲线，其曲线具有正常的规范模型，而曲线的曲线则更糟的是，其非gorenstein点的曲线更糟。基于这些工作，我们解决了一般情况的组合，并扩展了任何积分曲线的结果。
Max Noether's Theorem asserts that if $ω$ is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms $\text{Sym}^nH^0(ω)\to H^0(ω^n)$ are surjective for all $n\geq 1$. The result was extended for Gorenstein curves by many different authors in distinct ways. More recently, it was proved for curves with projectively normal canonical models, and curves whose non-Gorenstein points are bibranch at worse. Based on those works, we address the combinatorics of the general case and extend the result for any integral curve.
