Quasi-Homogeneous Linear Systems on P^2 with Base Points of Multiplicity 6

TL;DR

This paper proves the Harbourne-Hirschowitz conjecture for a specific class of linear systems on the projective plane with multiplicity 6, using degeneration techniques and prior results, leading to a classification of special systems.

Contribution

It establishes the conjecture for quasi-homogeneous systems with multiplicity 6 and provides a classification of these special systems, advancing understanding in algebraic geometry.

Findings

Proof of the Harbourne-Hirschowitz conjecture for multiplicity 6 systems

Classification of special systems with multiplicity 6

Application of degeneration methods and previous results

Abstract

In this paper we prove the Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems of multiplicity 6 on P^2. For the proof we use the degeneration of the plane by Ciliberto and Miranda and results by Laface, Seibert, Ugaglia and Yang. As an application we derive a classification of the special systems of multiplicity 6.