A +line is a scheme R ⊂ ℙr with a line as its reduction L = Rred which is the union of L and a tangent vector v ⊈ L with vred ∈ L. Here we prove in arbitrary characteristic that for r ≥ 4 a general union of lines and +lines has maximal rank. We use the case r = 3 proved by myself in a previous paper and adapt the characteristic zero proof of the case r > 3 given in the same paper.
@article{2065,
title = {Postulation of general unions of lines and +lines in positive characteristic},
journal = {CUBO, A Mathematical Journal},
volume = {20},
year = {2018},
doi = {10.4067/S0719-06462018000300031},
language = {en},
url = {http://dml.mathdoc.fr/item/2065}
}
Ballico, E. Postulation of general unions of lines and +lines in positive characteristic. CUBO, A Mathematical Journal, Tome 20 (2018) . doi : 10.4067/S0719-06462018000300031. http://gdmltest.u-ga.fr/item/2065/