NOT ALL FREE ARRANGEMENTS ARE K ( n , 1 ) PAUL
نویسندگان
چکیده
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 introduction Let si be a finite set of hyperplanes (subspaces of codimension one) passing through the origin in Rd . The complexification of the arrangement si is the arrangement of hyperplanes in Cd defined by
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