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Article Dans Une Revue Journal of Commutative Algebra Année : 2022

Unexpected curves in $\mathbb{P}^2$, line arrangements, and minimal degree of Jacobian relations

Alexandru Dimca

Résumé

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 $\mathbb{P}^2$, using the minimal degree of a Jacobian syzygy of the defining equation for the dual line arrangement $\mathcal A_Z$. 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.

Dates et versions

hal-03531314 , version 1 (18-01-2022)

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Alexandru Dimca. Unexpected curves in $\mathbb{P}^2$, line arrangements, and minimal degree of Jacobian relations. Journal of Commutative Algebra, inPress. ⟨hal-03531314⟩
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