具有预定角性曲线上的线性合点
Linear syzygies on curves with prescribed gonality
摘要：
本文证明了两个关于定角曲线的最小自由分解的线性链的命题。首先证明了亏格为g的一般曲线C满足Schreyer猜想，即\leq（C，K_C）=g-k，其所有的最高阶线性syzygon-Northcott型.这是一个超越格林猜想的陈述，并预言C的正则嵌入中的所有最高阶线性合宿由包含C的（k-1）维涡卷的合宿确定。其次，我们提出了一个最优的有效版本的Gonality猜想，并证明了它对一般的k-milling曲线。这推广了Ein-Lazarsfeld证明的渐近性猜想，改进了Rathmann在C是一般固定性曲线的情形下的结果.
英文摘要：
We prove two statements concerning the linear strand of the minimal free resolution of a curve of fixed gonality. Firstly, we show that a general curve C of genus g of non-maximal gonality k\leq (g+1)/2 satisfies Schreyer's Conjecture, that is, b_{g-k,1}(C,K_C)=g-k, and all its highest order linear syzygies are of Eagon-Northcott type. This is a statement going beyond Green's Conjecture and predicts that all highest order linear syzygies in the canonical embedding of C are determined by the syzygies of the (k-1)-dimensional scroll containing C. Secondly, we formulate an optimal effective version of the Gonality Conjecture and prove it for general k-gonal curves. This generalizes the asymptotic Gonality Conjecture proved by Ein-Lazarsfeld and improves results of Rathmann in the case where C is a general curve of fixed gonality.
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