Syzygies of projective varieties of large degree: Recent progress and open problems
Syzygies of projective varieties of large
degree: Recent progress and open problems
复制标题
大阶射影簇的对称性：最新进展和未解决的问题
作者：
L. Ein;R. Lazarsfeld
本文综述了近年来关于光滑复射影簇的合轨随嵌入线丛的正性增长的渐近行为的研究工作。
在快速概述了20世纪80年代和90年代关于分辨率的前几项的线性度的结果之后，我们讨论了一个非零定理，从渐近的角度来看，基本上所有可能为非零的合合模实际上都是非零的。我们解释了Erman和作者在Veronese簇的情况下对这个结果的快速新证明，并探讨了Betti数的渐近性的一些结果和定理。最后讨论了权为1的合点图的情形，以及关于大次曲线的合点图的共角性猜想。
博览会还讨论了许多悬而未决的问题和猜想。
This paper is a survey of recent work on the asymptotic behavior of the syzygies of a smooth complex projective variety as the positivity of the embedding line bundle grows.
After a quick overview of results from the 1980s and 1990s concerning the linearity of the first few terms of a resolution, we discuss a non-vanishing theorem to the effect that from an asymptotic viewpoint, essentially all of the syzygy modules that could be non-zero are in fact non-zero. We explain the quick new proof of this result in the case of Veronese varieties due to Erman and authors, and we explore some results and conjectures about the asymptotics of Betti numbers. Finally we discuss the case of syzygies of weight one, and the gonality conjecture on the syzygies of curves of large degree.
The exposition also discusses numerous open questions and conjectures.
通用格林拉扎斯菲尔德割线猜想
影响因子：
3.1
作者：
Farkas;Gavril;Kemeny;Michael
通讯作者：
Michael