On linear systems of P3 with nine base points
journal contributionposted on 07.11.2016 by Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel
Any type of content formally published in an academic journal, usually following a peer-review process.
© 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.
- Mathematical Sciences