Freeness of conic-line arrangements in P2

Hal Schenck, Ştefan O. Tohǎneanu

Research output: Contribution to journalArticlepeer-review


Let ζ = ∪ni=1 Ci C 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 (ζ) of logarithmic differential forms with pole along ζ. We also show that the analog of Terao's conjecture (freeness of Ω1 (ζ) is combinatorially determined if ζ is a union of lines) is false in this setting.

Original languageEnglish (US)
Pages (from-to)235-258
Number of pages24
JournalCommentarii Mathematici Helvetici
Issue number2
StatePublished - 2009


  • Curve arrangement
  • Line arrangement
  • Module of derivations

ASJC Scopus subject areas

  • General Mathematics


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