| Dolgachev (2005) associates to any reduced hyperplane arrangement A a natural subsheaf of the sheaf of logarithmic one-forms with poles along A. The sheaves of logarithmic differential forms with poles along a divisor were defined by Deligne (1970) for a divisor with normal crossing and by Saito (1980) for an arbitrary divisor. I will characterize which arrangements are Torelli, in other words when A can be reconstructed from the Dolgachev sheaf. This is joint work with D. Faenzi (Pau) and D. Matei (Bucharest). |