The orlik-terao algebra and 2-formality

Hal Schenck, Ştefan O. Tohãneanu

Research output: Contribution to journalArticlepeer-review

Abstract

The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A ⊂ ℂn it is the quotient of an exterior algebra A(V) on |A| generators. In [9], Orlik and Terao introduced a commutative analog Sym(V*)/I of the Orlik-Solomon algebra to answer a question of Aomoto and showed the Hubert series depends only on the intersection lattice L(A). In [6], Falk and Randell define the property of 2-formality; in this note we study the relation between 2-formality and the Orlik-Terao algebra. Our main result is a necessary and sufficient condition for 2-formality in terms of the quadratic component I2 of the Orlik-Terao ideal I. The key is that 2-formality is determined by the tangent space T p(V(I2)) at a generic point p.

Original languageEnglish (US)
Pages (from-to)171-182
Number of pages12
JournalMathematical Research Letters
Volume16
Issue number1
DOIs
StatePublished - Jan 2009

Keywords

  • Free resolution
  • Hyperplane arrangement
  • Orlik-terao algebra

ASJC Scopus subject areas

  • Mathematics(all)

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