Abstract:

Abstract: The Orlik-Terao algebra of a hyperplane arrangement is the algebra of the rational functions with poles on an arrangement of hyperplanes. This is a commutative analogue of the cohomology algebra of the complement and defines the so-called reciprocal plane which is a an irreducible projective variety. In a recent joint work with G. Denham and S. Tohaneanu, we give a decomposition result about the OT algebra whenever the underlying combinatorics has a certain genericity structure. This result implies that the OT algebra is Koszul if the arrangement is nicely filtered. As consequences, we give several other results such as characterizations for the OT algebra to be a quadratic complete intersection.