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

Daniele Faenzi (1) , Jean Vallès (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We propose an approach to study logarithmic sheaves T P n (− log DA) 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.

Domaines: Géométrie algébrique [math.AG]

Daniele Faenzi, Jean Vallès. Logarithmic bundles and line arrangements, an approach via the standard construction. Journal of the London Mathematical Society, 2014, 90 (3), pp.675-694. ⟨10.1112/jlms/jdu046⟩. ⟨hal-01993903⟩