On a notion of speciality of linear systems in P^n
Algebraic Geometry
2015-10-01 v2 Commutative Algebra
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.
Cite
@article{arxiv.1210.5175,
title = {On a notion of speciality of linear systems in P^n},
author = {Maria Chiara Brambilla and Olivia Dumitrescu and Elisa Postinghel},
journal= {arXiv preprint arXiv:1210.5175},
year = {2015}
}
Comments
26 pages. Minor changes, Definition 3.2 slightly extended. Accepted for publication in Transactions of AMS