关于平面曲线的雅可比矩阵的希尔伯特向量

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2019-05-10 DOI:10.4171/pm/2038

Armando Cerminara, A. Dimca, G. Ilardi

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引用次数: 6

摘要

我们确定了几类曲线$C:f=0$，其中Jacobian模$N（f）$的Hilbert向量可以完全确定，即只有有理不可约分量的3-yzygy曲线、最大Tjurina曲线和节点曲线。利用Hartshorne关于$\mathbb｛P｝^2$上一些秩为2的向量丛的上同调的一个结果，在半稳定性条件下，得到了Jacobian模$N（f）$的初始阶的一个尖锐下界。

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On the Hilbert vector of the Jacobian module of a plane curve

We identify several classes of curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 vector bundles on $\mathbb{P}^2$, is used to get a sharp lower bound for the initial degree of the Jacobian module $N(f)$, under a semistability condition.

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.