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arXiv · 1410.8065

On linear systems of $\mathbb{P}^3$ with nine base points

Maria Chiara Brambilla·Olivia Dumitrescu·Elisa Postinghel
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Abstract

We study special linear systems of surfaces of $\mathbb{P}^3$ 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 $\mathbb{P}^2$ 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.

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Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel. 2014-10-29. On linear systems of $\mathbb{P}^3$ with nine base points. https://doi.org/10.1007/s10231-015-0528-5

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