Freeness of conic-line arrangements in

  • Henry K. Schenck

    University of Illinois, Urbana, United States
  • Ştefan O. Tohǎneanu

    University of Cincinnati, United States


Let 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 of logarithmic differential forms with pole along . We also show that the analog of Terao’s conjecture (freeness of is combinatorially determined if is a union of lines) is false in this setting.

Cite this article

Henry K. Schenck, Ştefan O. Tohǎneanu, Freeness of conic-line arrangements in . Comment. Math. Helv. 84 (2009), no. 2, pp. 235–258

DOI 10.4171/CMH/161