Elementary modifications and line configurations in ℙ2

Henry Koewing Schenck

Research output: Contribution to journalArticle

Abstract

Associated to a projective arrangement of hyperplanes A ⊆ P n is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in ℙ2. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regularity of D(A). We also give simple combinatorial conditions for the associated bundle to be stable, and describe its jump lines. These regularity bounds and stability considerations impose constraints on Terao's conjecture.

Original languageEnglish (US)
Pages (from-to)447-462
Number of pages16
JournalCommentarii Mathematici Helvetici
Volume78
Issue number3
DOIs
StatePublished - Sep 1 2003

Keywords

  • Castelnuovo-Mumford regularity
  • Hyperplane arrangement
  • Jump locus
  • Stability
  • Vector bundle

ASJC Scopus subject areas

  • Mathematics(all)

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