Author:

Keywords:

Linear systems, Fat points, Base locus, Science & Technology, Physical Sciences, Mathematics, fat points, base locus, linear speciality, effective cone, THIN ALGEBRAS, DIVISORS, POINTS, 0101 Pure Mathematics, 0102 Applied Mathematics, General Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

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.