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Title: On the Effective Cone of Pn Blown-up at n + 3 Points
Authors: Brambilla, Maria Chiara
Dumitrescu, Olivia
Postinghel, Elisa
Keywords: Froberg–Iarrobino conjectures
Effective and movable cones
Rational normal curve
Secant varieties
Issue Date: 2016
Publisher: © Taylor & Francis
Citation: BRAMBILLA, M.C., DUMITRESCU, O. and POSTINGHEL, E., 2016. On the Effective Cone of Pn Blown-up at n + 3 Points. Experimental Mathematics, 25(4), pp. 452-465.
Abstract: © 2016 Taylor & Francis.We compute the facets of the effective and movable cones of divisors on the blow-up of ℙn at n + 3 points in general position. Given any linear system of hypersurfaces of ℙn based at n + 3 multiple points in general position, we prove that the secant varieties to the rational normal curve of degree n passing through the points, aswell as their joinswith linear subspaces spanned by some of the points, are cycles of the base locus andwe compute their multiplicity.We conjecture that a linear systemwith n + 3 points is linearly special only if it contains such subvarieties in the base locus and we give a new formula for the expected dimension.
Description: This is an Accepted Manuscript of an article published by Taylor & Francis in Experimental Mathematics on 06 Apr 2016, available online: http://dx.doi.org/10.1080/10586458.2015.1099060
Version: Accepted for publication
DOI: 10.1080/10586458.2015.1099060
URI: https://dspace.lboro.ac.uk/2134/23073
Publisher Link: http://dx.doi.org/10.1080/10586458.2015.1099060
ISSN: 1058-6458
Appears in Collections:Published Articles (Maths)

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