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On the Effective Cone of Pn Blown-up at n + 3 Points

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posted on 07.11.2016, 10:03 by Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel
© 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Experimental Mathematics

Volume

25

Issue

4

Pages

452 - 465

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.

Publisher

© Taylor & Francis

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016-04-06

Notes

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

ISSN

1058-6458

eISSN

1944-950X

Language

en