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Title: On linear systems of P3 with nine base points
Authors: Brambilla, Maria Chiara
Dumitrescu, Olivia
Postinghel, Elisa
Keywords: Fat points
Degeneration techniques
Laface–Ugaglia Conjecture
Base locus
Quadric surface
Issue Date: 2016
Publisher: © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag
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.
Abstract: © 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.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-015-0528-5
Version: Accepted for publication
DOI: 10.1007/s10231-015-0528-5
URI: https://dspace.lboro.ac.uk/2134/23077
Publisher Link: http://dx.doi.org/10.1007/s10231-015-0528-5
ISSN: 0373-3114
Appears in Collections:Published Articles (Maths)

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