Nets in P^2 and Alexander Duality

• A net in P^2 is a configuration of lines A and points X satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac–Moody algebras to cohomology jump loci of hyperplane arrangements. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank ≤r. In the context of line arrangements in P^2, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)