Mathematics – Commutative Algebra
Scientific paper
2009-01-02
Mathematical Research Letters, 16 (2009), 171-182
Mathematics
Commutative Algebra
11 pages, 2 figures. v2 typo in Example 1.4 fixed
Scientific paper
The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A in C^n; it is the quotient of an exterior algebra E(V) on |A| generators. Orlik and Terao introduced a commutative analog S(V)/I of the Orlik-Solomon algebra to answer a question of Aomoto and showed the Hilbert series depends only on the intersection lattice L(A). Motivated by topological considerations, Falk and Randell introduced the property of 2-formality; 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: 2-formality is determined by the tangent space T_p(V(I_2)) at a generic point p.
Schenck Hal
Tohaneanu Stefan
No associations
LandOfFree
The Orlik-Terao algebra and 2-formality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Orlik-Terao algebra and 2-formality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Orlik-Terao algebra and 2-formality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380946