Related papers: On linear systems of P^3 through multiple points
In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.
Consider a (non-empty) linear system of surfaces of degree d in P^3 through at most 8 multiple points in general position and let L denote the corresponding complete linear system on the blowing-up X of P^3 along those general points. Then…
In this note we relate about the problem of evaluate the dimension of linear systems through fat points defined on generic $K3$ surfaces.
We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the cases that have not been completed in a paper by E. Ballico…
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…
In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.
We enumerate the number of surfaces of degree $d$ in $P^3$ having a singular line of order $k$, passing through $\delta$ generic points (where $\delta$ is the dimension of moduli space of such surfaces).
We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general positions. As an application we obtain a classification of special linear systems on P1xP1 for which the multiplicities…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
Given a surface S in P^3 and a collection of general points on it, how many surfaces of a given degree intersect S in a curve with prescribed multiplicities at the points? We formulate two natural conjectures which would answer this…
The main goal of this paper is to present an algorithm bounding the dimension of a linear system of curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Hirschowitz--Harbourne…
In this paper we compute upper bounds for the number of ordinary triple points on a hypersurface in $P^3$ and give a complete classification for degree six (degree four or less is trivial, and five is elementary). But the real purpose is to…
We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric…
In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least…
We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that…
We prove that the number of legendrian rational cubics in $\mathbb C P^3$ through three generic points and a line is three; also we classify all legendrian curves on a quadric surface. Several computations are additionally verified using…
We study linear systems of surfaces in $\mathbb{P}^3$ singular along general lines. Our purpose is to identify and classify special systems of such surfaces, i.e., those nonempty systems where the conditions imposed by the multiple lines…
In arXive:0705.3912 we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption,…
In this article we address the problem of computing the dimension of the space of plane curves of degree $d$ with $n$ general points of multiplicity $m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$, the dimension…
In this note we consider the behavior of linear systems of P^3 through fat points under a cubo-cubic Cremona transformation. This allows us to produce a class of special systems which we conjecture to be the only ones.