Vanishing theorems for linearly obstructed divisors Olivia Dumitrescu Elisa Postinghel 2134/23953 https://repository.lboro.ac.uk/articles/journal_contribution/Vanishing_theorems_for_linearly_obstructed_divisors/9387467 We study divisors on the blow-up of Pn at points in general position that are non-special with respect to the notion of linear speciality introduced in [6]. We describe the cohomology groups of their strict transforms via the blow-up of the space along their linear base locus. We extend the result to non-effective divisors that sit in a small region outside the effective cone. As an application, we describe linear systems of divisors in Pn blown-up at points in star configuration and their strict transforms via the blow-up of the linear base locus. 2017-02-01 14:39:40 Linear systems Fat points Base locus Linear speciality Effective cone Mathematical Sciences not elsewhere classified