2134/23953 Olivia Dumitrescu Olivia Dumitrescu Elisa Postinghel Elisa Postinghel Vanishing theorems for linearly obstructed divisors Loughborough University 2017 Linear systems Fat points Base locus Linear speciality Effective cone Mathematical Sciences not elsewhere classified 2017-02-01 14:39:40 Journal contribution 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.