Transactions of the American Mathematical Society vol:367 issue:8 pages:5447-5473
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.