On a notion of speciality of linear systems in ℙⁿ

Brambilla, M.; Dumitrescu, O.; Postinghel, E.

doi:10.1090/S0002-9947-2014-06212-0

On a notion of speciality of linear systems in $\mathbb {P}^n$
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by M. C. Brambilla, O. Dumitrescu and E. Postinghel PDF

Trans. Amer. Math. Soc. 367 (2015), 5447-5473 Request permission

Abstract:

Given a linear system in $\mathbb {P}^n$ 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 an arbitrary number of points and necessary conditions for a small number of points.

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