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On linear systems of P3 with nine base points

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journal contribution
posted on 07.11.2016 by Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel
© 2015, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.We study special linear systems of surfaces of P3 interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in terms of linear obstructions for a quasi-homogeneous class. By degeneration, we also prove a Nagata type result for the blown-up projective plane in points that implies a base locus lemma for the quadric. As an application, we establish Laface–Ugaglia Conjecture for linear systems with multiplicities bounded by 8 and for homogeneous linear systems with multiplicity m and degree up to 2 m+ 1.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Annali di Matematica Pura ed Applicata

Volume

195

Issue

5

Pages

1551 - 1574

Citation

BRAMBILLA, M.C., DUMITRESCU, O. and POSTINGHEL, E., 2016. On linear systems of P3 with nine base points. Annali di Matematica Pura ed Applicata, 195(5), pp. 1551-1574.

Publisher

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag

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

2015-09-04

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-015-0528-5

ISSN

0373-3114

eISSN

1618-1891

Language

en

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