未知的曲线，线的排列，以及雅可比矩阵关系的最小程度

Pub Date : 2023-03-01 DOI:10.1216/jca.2023.15.15

A. Dimca

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引用次数: 3

摘要

我们利用对偶线排列AZ的定义方程的雅可比合集的最小度，重新表述了Cook, Harbourne, Migliore和Nagel关于P2中一组点Z的非预期平面曲线的存在性和不可约性的基本结果。给出了这种新方法的几种应用。特别地，我们证明了不可约的非预期五项只有在集合Z的基数等于11或12时才可能发生，并描述了这种情况发生的五种情况。

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UNEXPECTED CURVES IN ℙ2, LINE ARRANGEMENTS, AND MINIMAL DEGREE OF JACOBIAN RELATIONS

We reformulate a fundamental result due to Cook, Harbourne, Migliore and Nagel on the existence and irreduciblity of unexpected plane curves of a set of points Z in P2, using the minimal degree of a Jacobian syzygy of the defining equation for the dual line arrangement AZ . Several applications of this new approach are given. In particular, we show that the irreducible unexpected quintics may occur only when the set Z has the cardinality equal to 11 or 12, and describe five cases where this happens.

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