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Article Dans Une Revue Journal of Algebraic Combinatorics Année : 2018

On supersolvable and nearly supersolvable line arrangements

Résumé

We introduce a new class of line arrangements in the projective plane, called nearly supersolvable, and show that any arrangement in this class is either free or nearly free. More precisely, we show that the minimal degree of a Jacobian syzygy for the defining equation of the line arrangement, which is a subtle algebraic invariant, is determined in this case by the combinatorics. When such a line arrangement is nearly free, we discuss the splitting types and the jumping lines of the associated rank two vector bundle, as well as the corresponding jumping points, introduced recently by S. Marchesi and J. Vall\`es.

Dates et versions

hal-01761545 , version 1 (09-04-2018)

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Alexandru Dimca, Gabriel Sticlaru. On supersolvable and nearly supersolvable line arrangements. Journal of Algebraic Combinatorics, 2018, ⟨10.1007/s10801-018-0859-6⟩. ⟨hal-01761545⟩
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