A rank two vector bundle associated to a three arrangement, and its chern polynomial

Henry K. Schenck

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the Poincaré polynomial π(A, t) of an essential, central three arrangement A over a field K of characteristic zero is (1+t)·ct(D0(A)), where D0(A) is the sheaf associated to the kernel of the Jacobian ideal of A, and ct is the Chern polynomial. This shows that a version of Terao's theorem [Invent. Math.63 (1981), 159-179] on free arrangements also holds for all three arrangements. We also prove that for such an arrangement D0(A) is a vector bundle on P2 and derive an algorithm which computes ct(D0(A)) from a free resolution of the Jacobian ideal of the defining polynomial of A.

Original languageEnglish (US)
Pages (from-to)214-229
Number of pages16
JournalAdvances in Mathematics
Volume149
Issue number2
DOIs
StatePublished - Feb 10 2000

ASJC Scopus subject areas

  • Mathematics(all)

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