On linear systems of P^3 with nine base points
On linear systems of P^3 with nine base points
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关于具有九个基点的 P^3 线性系统
DOI：
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发表时间：
2014
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通讯作者：
Elisa Postinghel
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作者：
M. Brambilla;Olivia Dumitrescu;Elisa Postinghel
我们研究了 P 3 表面的特殊线性系统，在一般位置上插值九个点，具有二次曲面作为固定分量。通过在放大空间中执行退化，我们将二次障碍解释为准同质类的线性障碍。通过退化，我们还证明了点放大投影平面的 Nagata 型结果，这暗示了二次曲面的基本轨迹引理。作为应用，我们针对重数为 8 的线性系统以及重数为 m 且次数高达 2 m + 1 的齐次线性系统建立了拉法斯-乌加利亚猜想。
We study special linear systems of surfaces of 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 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.