Projective normality and syzygies of algebraic surfaces
Projective normality and syzygies of algebraic surfaces
复制标题
代数曲面的射影正态性和共合性
DOI：
10.1515/crll.1999.506.145
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
B. P. Purnaprajna
中科院分区：
文献类型：
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作者：
F. Gallego;B. P. Purnaprajna
摘要在这项工作中，我们发展了计算几类簇的Koszul上同调群的新方法。作为应用，我们证明了关于代数曲面的射影正规性和合性的结果。从更一般的结果中，我们特别得到以下结果：关于Kodaira维为0的曲面的射影正规性和正规表示的Mukai猜想(及其更强的变种)，与伴随线性级数相关的高次合并界，关于正Kodaira维曲面的射影正规性和正规表示的Mukai猜想的有效界，以及关于一般类型曲面的射影正规性的结果(Ciliberto的恢复和加强结果)及其在更高合并度上的推广。此外，我们还将上述结果推广到奇异曲面上。
Abstract In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces. From more general results we obtain in particular the following: Mukai's conjecture (and stronger variants of it) regarding projective normality and normal presentation for surfaces with Kodaira dimension 0, and uniform bounds for higher syzygies associated to adjoint linear series, effective bounds along the lines of Mukai's conjecture regarding projective normality and normal presentation for surfaces of positive Kodaira dimension, and, results on projective normality for pluricanonical models of surfaces of general type (recovering and strengthening results by Ciliberto) and generalizations of them to higher syzygies. In addition, we also extend the above results to singular surfaces.