Complements of hypersurfaces, variation maps and minimal models of   arrangements
  We prove the minimality of the CW-complex structure for complements of hyperplane arrangements in $\mathbb C^n$ by using the theory of Lefschetz pencils and results on the variation maps within a pencil of hyperplanes. This also provides a method to compute the Betti numbers of complements of arrangements via global polar invariants. 
Mihai Tibar
math.AG math.CV