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.

On the effective cone of ℙn blown-up at n + 3 points / Brambilla, M. C.; Dumitrescu, O.; Postinghel, E.. - In: EXPERIMENTAL MATHEMATICS. - ISSN 1058-6458. - 2016, 25:4(2016), pp. 452-465. [10.1080/10586458.2015.1099060]

### On the effective cone of ℙn blown-up at n + 3 points

#### Abstract

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.
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2016
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Brambilla, M. C.; Dumitrescu, O.; Postinghel, E.
On the effective cone of ℙn blown-up at n + 3 points / Brambilla, M. C.; Dumitrescu, O.; Postinghel, E.. - In: EXPERIMENTAL MATHEMATICS. - ISSN 1058-6458. - 2016, 25:4(2016), pp. 452-465. [10.1080/10586458.2015.1099060]
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Open Access dal 01/01/2018

Tipologia: Post-print referato (Refereed author’s manuscript)
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11572/274847`