Lagrangian fibration structure on the cotangent bundle of a del Pezzo surface of degree 4

TL;DR

This paper demonstrates a natural Lagrangian fibration on the cotangent bundle of a degree 4 del Pezzo surface and explicitly describes its level surfaces, contributing to the understanding of geometric structures on such surfaces.

Contribution

It establishes a natural Lagrangian fibration on the cotangent bundle of degree 4 del Pezzo surfaces and explicitly characterizes all level surfaces of this map.

Findings

Existence of a natural Lagrangian fibration on the cotangent bundle.

Explicit description of all level surfaces of the fibration.

Enhanced understanding of geometric structures on del Pezzo surfaces.

Abstract

In this paper, we show that there is a natural Lagrangian fibration structure on the map $\Phi$ from the cotangent bundle of a del Pezzo surface $X$ of degree 4 to $\mathbb C^2$. Moreover, we describe explicitly all level surfaces of the above natural map $\Phi$.