POSTINGHEL, E. and DUMITRESCU, O., 2017. Vanishing theorems for linearly obstructed divisors. Journal of Algebra, 477 (May), pp.312-359.
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 . 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.
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The authors thank the organisors of the Workshop on Perspectives and Emerging Topics in Algebra and Combinatorics -PEAKs 2013 (Austria), funded by DFG Conference Grant HA4383/6-1 for the hospitality during their stay that promoted and made this collaboration possible.