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

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.

24 pages. Minor changes. To appear in Annali di Matematica Pura ed Applicata

References in corpus (5)

• Vanishing theorems for linearly obstructed divisors
• On a class of special linear systems of P^3
• On linear systems of P^3 through multiple points
• On the effective cone of ${\mathbb{P}}^n$ blown-up at $n+3$ points
• Standard classes on the blow-up of P^n at points in very general position

Cited by in corpus (4)

• Positivity of divisors on blown-up projective spaces, II
• On the effective cone of ${\mathbb{P}}^n$ blown-up at $n+3$ points
• Collisions of fat points and applications to interpolation theory
• Weyl cycles on the blow-up of ${\mathbb{P}}^4$ at eight points