Logarithmic sheaves and arrangements of hyperplanes
speaker: Daniel Matei (IMAR)abstract: We discuss the sheaves of logarithmic one-forms introduced recently by I. Dolgachev. To a divisor on a smooth variety is associated a certain sub-sheaf of the sheaf of logarithmic one forms considered by K.Saito. The latter sheaf coincides with the double dual of the former. In the particular case where the divisor is an arrangement of hyperplanes in the projective space, the sub-sheaf turns out to be a Steiner sheaf, possesing a certain type of resolution. M. Kapranov and I. Dolgachev, and later J. Valles, studied the case of generic arrangements, for which the sheaves in question are in fact locally free. They proved that two arrangements with isomorphic bundles of logarithmic one-forms coincide unless they osculate a normal rational curve. Motivated by a conjecture of I. Dolgachev, we address here the similar problem for arbitrary hyperplane arrangements, that is to what extent the above Steiner logarithmic sheaf determines the arrangement. This is a joint work with D. Faenzi and J. Valles.
timetable:
Fri 25 Jun, 9:00 - 10:00, Aula Dini
documents:
Daniel Matei
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