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• W2024674837 abstract "Let A be an n × d matrix having full rank n. An orthogonal dual A⊥ of A is a (d-n) × d matrix of rank (d−n) such that every row of A⊥ 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 × d matrix of coefficients of the homogeneous linear forms for which the hyperplanes are kernels. When n ≥ 5, we show that if the matroid (or the lattice of intersection) of an n-dimensional essential arrangement $${mathcal A}$$ contains a modular copoint whose complement spans, then the derivation module of the orthogonally dual arrangement $${mathcal A}$$ ⊥ has projective dimension at least ⌈ n(n+2)/4 ⌉ - 3." @default.
• W2024674837 created "2016-06-24" @default.
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• W2024674837 date "2006-07-11" @default.
• W2024674837 modified "2023-10-04" @default.
• W2024674837 title "Derivation modules of orthogonal duals of hyperplane arrangements" @default.
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• W2024674837 doi "https://doi.org/10.1007/s10801-006-0023-6" @default.
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