Free but not recursively free arrangements

NOT ALL FREE ARRANGEMENTS ARE K ( n , 1 ) PAUL

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is K(n, 1 ). These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well. I. Definitions and ...

Matroid Representations and Free Arrangements

We show that Terao's Conjecture ("Freeness of the module of logarithmic forms at a hyperplane arrangement is determined by its abstract matroid") holds over fields with at most four elements. However, an example demonstrates that the field characteristic has to be fixed for this. 1. Free arrangements The present study continues an investigation of the connection between algebraic and combinator...

Chern Classes of Free Hypersurface Arrangements

The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally analytically isomorphic to free hyperplane arrangements.

Ravels: knot-free but not free. Novel entanglements of graphs in 3-space

Perhaps Not a Free Lunch But At Least a Free Appetizer

This work is a product of the Collaborative Research Center 531, \Computational Intelligence", at the University of Dortmund and was printed with nancial support of the Deutsche Forschungsgemeinschaft. Abstract It is often claimed that Evolutionary Algorithms are superior to other optimization techniques, in particular, in situations where not much is known about the objective function to be op...