For line arrangements, the minimal degree of a logarithmic derivation changes predictably under adding or deleting one line, yielding new maximal Tjurina arrangements and a sharp n3≤5 combinatoriality threshold.
Triangular arrangements on the projective plane
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abstract
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not.
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2019 1verdicts
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Addition-deletion results for the minimal degree of logarithmic derivations of arrangements
For line arrangements, the minimal degree of a logarithmic derivation changes predictably under adding or deleting one line, yielding new maximal Tjurina arrangements and a sharp n3≤5 combinatoriality threshold.