论文标题
关于Lazarsfeld的Castelnuovo-Mumford规律性的评论
A Remark on Lazarsfeld's Approach to Castelnuovo-Mumford Regularity
论文作者
论文摘要
我们为Castelnuovo-Mumford的规律性提供了新的界限，该规律性的理想支架是任何维度的复杂投影歧管。它们线性地依赖于希尔伯特多项式的系数，并且对于有理卷轴是最佳的，但很可能不是其他品种。我们的证明是基于对拉扎尔斯菲尔德（Lazarsfeld）的表面方法的观察，并且不需要（完整的）投影步骤。只要在一般投影的纤维上，我们就可以为给定品种的每个部分线性投影获得一个结合。
We derive new bounds for the Castelnuovo-Mumford regularity of the ideal sheaf of a complex projective manifold of any dimension. They depend linearly on the coefficients of the Hilbert polynomial, and are optimal for rational scrolls, but most likely not for other varieties. Our proof is based on an observation of Lazarsfeld in his approach for surfaces and does not require the (full) projection step. We obtain a bound for each partial linear projection of the given variety, as long as a certain vanishing condition on the fibers of a general projection holds.
