关于代数曲线简单覆盖的Green和Green-Lazarfeld图
On Green and Green-Lazarfeld conjectures for simple coverings of algebraic curves
摘要：
设X是一条光滑亏格g曲线，它具有一个简单态射f：X -> C，其中C是一条射影直线，或者更一般地说，C是任何一条平滑曲线，它的角度是用许多铅笔计算的。在这里，我们应用Aprodu开发的一种方法来证明，如果g足够大，那么X满足格林和格林-拉扎斯菲尔德拓扑。我们也部分解决的情况下，其中的gonality的C是计算无限多铅笔。
英文摘要：
Let X be a smooth genus g curve equipped with a simple morphism f: X -> C, where C is either the projective line or more generally any smooth curve whose gonality is computed by finitely many pencils. Here we apply a method developed by Aprodu to prove that if g is big enough then X satisfies both Green and Green-Lazarsfeld conjectures. We also partially address the case in which the gonality of C is computed by infinitely many pencils.
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