Derivation modules of orthogonal duals of hyperplane arrangements

Details Derivation modules of orthogonal duals of hyperplane arrangements Derivation modules of orthogonal duals of hyperplane arrangements

2006-04-07

arxiv.org/abs/math/0604168v1

Journal of Algebraic Combinatorics, 24, (2006), 253-262

Mathematics

Combinatorics

9 pages 2 figures

Scientific paper

Let A be an n by d matrix having full rank n. An orthogonal dual A^{\perp} of A is a (d-n) by d matrix of rank (d-n) such that every row of A^{\perp} is orthogonal (under the usual dot product) to every row of A. We define the orthogonal dual for arrangements by identifying an essential (central) arrangement of d hyperplanes in n-dimensional space with the n by d matrix of coefficients of the homogeneous linear forms for which the hyperplanes are kernels. If n is at least 5, we show that if the matroid (or the intersection lattice) of an n-dimensional essential arrangement A contains a modular copoint whose complement spans, then the derivation module of the orthogonally dual arrangement \A^{\perp} has projective dimension at least [n(n+2)/4] - 3,([ ] denotes ceiling).

Affiliated with

Also associated with

No associations

Rating

Derivation modules of orthogonal duals of hyperplane arrangements 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 Derivation modules of orthogonal duals of hyperplane arrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Derivation modules of orthogonal duals of hyperplane arrangements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-723434