Torelli problem on logarithmic sheaves

Abstract: The logarithmic sheaf associated to a reduced divisor, is the sheaf of differential 1-forms with logarithmic poles along the divisor, and it was introduced by P. Deligne to define a mixed Hodge structure on the complement of the divisor. There have been a great deal of study on this subject, and one of the questions is whether the sheaf determines the divisor or not, which we call the Torelli problem. In case of general hyperplane arrangements on projective spaces, I. Dolgachev and M. Kapranov gave a positive answer to the Torelli problem when the number of hyperplanes is big enough, and then later J. Valles gave a complete answer. In this talk we give several other results on the Torelli problem, and report our recent result, in which we introduce two different approachs to have a positive answer on the problem. This is a joint work with S. Marchesi, J. Pons-Llopis and J. Valles.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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