Fiber sums of genus 2 Lefschetz fibrations

TL;DR

This paper demonstrates that any genus 2 Lefschetz fibration can be made holomorphic through fiber summation with a holomorphic fibration, leveraging recent results on their holomorphicity.

Contribution

It introduces a method to convert any genus 2 Lefschetz fibration into a holomorphic one via fiber sum, based on recent holomorphicity results.

Findings

Any genus 2 Lefschetz fibration becomes holomorphic after fiber sum.

Utilizes recent results of Siebert and Tian on holomorphicity.

Provides a technique to modify fibrations to achieve holomorphicity.

Abstract

Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.