The gonality conjecture on syzygies of algebraic curves of large degree
The gonality conjecture on syzygies of algebraic curves of large degree
复制标题
大次代数曲线共性的棱性猜想
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
R. Lazarsfeld
中科院分区：
文献类型：
--
作者：
L. Ein;R. Lazarsfeld
我们表明，一个小的变化所使用的方法Voisin在她的研究规范曲线导致一个令人惊讶的快速证明的gonality猜想的绿色和第二作者，声称可以读出的gonality曲线C从其决议中的嵌入定义的任何一个线丛足够大的程度。更一般地，我们建立了C上任意线丛所对应的模的权一合轨渐近为零的充分必要条件。
We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting that one can read off the gonality of a curve C from its resolution in the embedding defined by any one line bundle of sufficiently large degree. More generally, we establish a necessary and sufficient condition for the asymptotic vanishing of the weight one syzygies of the module associated to an arbitrary line bundle on C.