Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces

TL;DR

This paper classifies webs of minimal degree rational curves on surfaces and the Neron-Severi lattices of real weak del Pezzo surfaces, linking these classifications to root subsystems of E8.

Contribution

It provides a new classification of webs of rational curves and Neron-Severi lattices for real weak del Pezzo surfaces, connecting geometric structures to algebraic root systems.

Findings

Classification of webs of minimal degree rational curves

Criterion for webs being hexagonal

Classification of Neron-Severi lattices of real weak del Pezzo surfaces

Abstract

We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo surfaces. These two classifications are related to root subsystems of E8.