9 points in P3.pdf (466.15 kB)
Download fileOn linear systems of P3 with nine base points
journal contribution
posted on 07.11.2016, 11:01 authored 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.
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