10 citations · 10 across the 2 of their papers we have counts for
6 papers · 1 filter
The line geometry of resonance varieties
Michael Falk
Let R^1(A,R) be the degree-one resonance variety over a field R of a hyperplane arrangement A. We give a geometric description of R^1(A,R) in terms of projective line complexes. Th…
Line-closed matroids, quadratic algebras, and formal arrangements
Michael Falk
Let be a matroid on ground set \A. The Orlik-Solomon algebra is the quotient of the exterior algebra \E on \A by the ideal \I generated by circuit boundaries. The quadra…
Combinatorial and algebraic structure in Orlik-Solomon algebras
Michael Falk
The Orlik-Solomon algebra of a matroid is the free exterior algebra on the points, modulo the ideal generated by the circuit boundaries. On one hand, this algebra…
On the homotopy theory of arrangements, II
Michael Falk, Richard Randell
In "On the homotopy theory of arrangements," published in 1986, the authors gave a comprehensive survey of the subject. This article updates and continues the earlier article, noti…
Parallel connections and bundles of arrangements
Michael J. Falk, Nicholas J. Proudfoot
Let \A be a complex hyperplane arrangement, and let be a modular element of arbitrary rank in the intersection lattice of \A. We show that projection along restricts to a f…
Orlik-Solomon algebras and Tutte polynomials
Carrie Eschenbrenner, Michael Falk
The algebra of a matroid is a graded algebra related to the Whitney homology of the lattice of flats of . In case is the underlying matroid of a hyperplane arra…