Logarithmic bundles and line arrangements, an approach via the standard construction

摘要

We propose an approach to study logarithmic sheaves T_(Pn)(-logD_A) associated with hyperplane arrangements A on the projective space P~n, based on projective duality, direct image functors and vector bundles methods. We focus on free line arrangements admitting a point with high multiplicity, or having low exponents, proving Terao's conjecture in this range.