Terao's conjecture for triangular arrangements
Marchesi, Simone ; Vallès, Jean
arXiv, Tome 2019 (2019) no. 0, / Harvested from
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 of this arrangement is associated to another one with the same combinatorics, constructed by removing lines to a Ceva arrangement. We then characterize the freeness of such triangular arrangements, which will depend on the combinatorics of the deleted lines. We give two triangular arrangements having the same weak combinatorics (that means the same number $t_i$ of points with multiplicity $i, i\ge 2$), such that one is free but the other one is not. Finally, we prove that Terao's conjecture holds for triangular arrangement.
Publié le : 2019-03-21
Classification:  Mathematics - Algebraic Geometry,  Mathematics - Algebraic Topology,  Mathematics - Combinatorics,  52C35, 14F05, 32S22 
@article{1903.08885,
     author = {Marchesi, Simone and Vall\`es, Jean},
     title = {Terao's conjecture for triangular arrangements},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1903.08885}
}

Marchesi, Simone; Vallès, Jean. Terao's conjecture for triangular arrangements. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1903.08885/