Commentarii Mathematici Helvetici

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Volume 84, Issue 2, 2009, pp. 235–258
DOI: 10.4171/CMH/161

Published online: 2009-06-30

Freeness of conic-line arrangements in ℙ2

Henry K. Schenck[1] and Ştefan O. Tohǎneanu[2]

(1) University of Illinois, Urbana, United States
(2) University of Cincinnati, United States

Let C = ni = 1 Ci ⊆ ℙ2 be a collection of smooth rational plane curves. We prove that the addition–deletion operation used in the study of hyperplane arrangements has an extension which works for a large class of arrangements of smooth rational curves, giving an inductive tool for understanding the freeness of the module Ω1(C) of logarithmic differential forms with pole along C. We also show that the analog of Terao’s conjecture (freeness of Ω1(C) is combinatorially determined if C is a union of lines) is false in this setting.

Keywords: Line arrangement, curve arrangement, module of derivations

Schenck Henry, Tohǎneanu Ştefan: Freeness of conic-line arrangements in ℙ2. Comment. Math. Helv. 84 (2009), 235-258. doi: 10.4171/CMH/161