论文标题
通用割线束和典型曲线的共同体
Universal Secant Bundles and Syzygies of Canonical Curves
论文作者
论文摘要
我们介绍了EIN，Green和Lazarsfeld使用的割线束带的相对化，并将这种结构应用于规范曲线的Syzygies的研究。作为第一个应用程序，我们为一般规范曲线提供了更简单的Voisin定理证明。这完全决定了此类曲线的坐标环的最小自由分辨率的术语。其次，对于偶数属的曲线，我们通过为最后一个syzygy空间提供结构定理来增强Voisin定理，从而解决了几何syzygy猜想，偶数属。
We introduce a relativization of the secant sheaves used by Ein, Green and Lazarsfeld and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Secondly, in the case of curves of even genus, we enhance Voisin's Theorem by providing a structure theorem for the last syzygy space, resolving the Geometric Syzygy Conjecture in even genus.
