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 2m+1.
On linear systems of P3 with nine base points
BRAMBILLA, Maria Chiara;
2016-01-01
Abstract
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 2m+1.File in questo prodotto:
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