Del Pezzo surfaces of degree one and examples of Zariski multiples

TL;DR

This paper constructs large Zariski N-tuples on degree one del Pezzo surfaces by leveraging the Weyl group E8's monodromy action on 240 lines.

Contribution

It introduces a novel method to generate Zariski N-tuples using monodromy actions on del Pezzo surfaces of degree one.

Findings

Successfully constructed large Zariski N-tuples.

Demonstrated the role of Weyl group E8 in these constructions.

Provided explicit examples of Zariski multiples.

Abstract

We construct examples of Zariski N-tuples with large N using the monodromy action of the Weyl group of type E8 on the set of 240 lines in a del Pezzo surface of degree one.