The canonical pencils on Horikawa surfaces

TL;DR

This paper computes and compares the monodromies of canonical Lefschetz pencils on two homeomorphic Horikawa surfaces, revealing they share the same monodromy groups and are connected via a partial twisting operation.

Contribution

It provides the first explicit calculation of monodromies for these surfaces and demonstrates their relation through a novel partial twisting technique.

Findings

The monodromy groups of the pencils are identical.

The pencils are related by a partial twisting operation.

The study advances understanding of Lefschetz pencils on complex surfaces.

Abstract

We calculate the monodromies of the canonical Lefschetz pencils on a pair of homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical pencils on these surfaces have the same monodromy groups, and are related by a "partial twisting" operation.