On a notion of speciality of linear systems in P^n

Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel

Published 2012-10-18, updated 2013-06-10Version 2

Given a linear system in P^n with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion giving sufficient conditions for a linear system to be linearly non-special for arbitrary number of points, and necessary conditions for small numbers of points.