## Abstract

The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A ⊂ ℂ^{n} 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 I_{2} of the Orlik-Terao ideal I. The key is that 2-formality is determined by the tangent space T _{p}(V(I_{2})) at a generic point p.

Original language | English (US) |
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Pages (from-to) | 171-182 |

Number of pages | 12 |

Journal | Mathematical Research Letters |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2009 |

Externally published | Yes |

## Keywords

- Free resolution
- Hyperplane arrangement
- Orlik-terao algebra

## ASJC Scopus subject areas

- Mathematics(all)