Zariski chambers on surfaces of high Picard number

TL;DR

This paper introduces an improved algorithm for computing Zariski chambers on algebraic surfaces, enabling analysis of high Picard number surfaces and application to the Segre-Schur quartic.

Contribution

The paper presents a more efficient algorithm for Zariski chamber computation, allowing analysis of surfaces with high Picard number and large chamber counts.

Findings

Algorithm significantly outperforms previous methods

Able to compute chambers on high Picard number surfaces

Successfully applied to Segre-Schur quartic

Abstract

We present an improved algorithm for the computation of Zariski chambers on algebraic surfaces. The new algorithm significantly outperforms the so far available method and allows therefore to treat surfaces of high Picard number, where huge chamber numbers occur. As an application, we efficiently compute the number of chambers supported by the lines on the Segre-Schur quartic.