Resumen de Logarithmic bundles of hypersurface arrangements in

Elena Angelini

• Let ={?1,…,?ℓ} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space ?? and let Ω1??(log) be the logarithmic bundle attached to it. Following (Ancona in Notes of a talk given in Florence, 1998), we show that Ω1??(log) admits a resolution of length 1 which explicitly depends on the degrees and on the equations of ?1,…,?ℓ . Then we prove a Torelli type theorem when all the ?? ’s have the same degree ? and ℓ≥(?+??)+3 : indeed, we recover the components of as unstable smooth hypersurfaces of Ω1??(log) . Finally we analyze the cases of one quadric and a pair of quadrics, which yield examples of non-Torelli arrangements. In particular, through a duality argument, we prove that two pairs of quadrics have isomorphic logarithmic bundles if and only if they have the same tangent hyperplanes.