Computational birational geometry of minimal rational surfaces

TL;DR

This paper develops algorithms to realize birational links of type II between minimal del Pezzo surfaces, contributing to the computational classification of minimal rational surfaces within algebraic geometry.

Contribution

It introduces algorithms for birational links of type II between minimal del Pezzo surfaces and integrates these into a Magma implementation, advancing computational approaches in the field.

Findings

Algorithms successfully realize links of type II

Implementation in Magma supports classification efforts

Enhances computational tools for algebraic surface theory

Abstract

The classification of minimal rational surfaces and the birational links between them by Iskovskikh, Manin and others is a well-known subject in the theory of algebraic surfaces. We explain algorithms that realise links of type II between minimal del Pezzo surfaces, one of the major classes of birational links, and we describe briefly how this fits into a large project to implement the results of Iskovskikh's programme in Magma.