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

被引：0

作者：

Dimca, Alexandru ^{[1
,2
]}

机构：

[1] Univ Cote Azur, Lab JA Dieudonne, CNRS, UMR 7351, Nice, Romania

[2] Sim Stoilow Inst Math, Bucharest, Romania

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2023年 / 15卷 / 01期

关键词：

unexpected curves; line arrangements; Jacobian syzygies; HYPERSURFACES; FREENESS;

D O I：

10.1216/jca.2023.15.15

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We reformulate a fundamental result due to Cook, Harbourne, Migliore and Nagel on the existence and irreducibility 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.

引用

页码：15 / 30

页数：16

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