An elliptic fibration arising from the Lagrange top and its monodromy

TL;DR

This paper studies an elliptic fibration derived from the Lagrange top, analyzing its discriminant locus, singular fibers, and monodromy using complex algebraic geometry techniques.

Contribution

It provides a detailed description and classification of the discriminant locus and singular fibers of the elliptic fibration associated with the Lagrange top, including monodromy analysis.

Findings

Explicit description of the discriminant locus

Complete classification of singular fibers

Monodromy representation of the elliptic fibration

Abstract

This paper is to investigate an elliptic fibration over $\mathbb{CP}^2$ arising from the Lagrange top from the viewpoint of complex algebraic geometry. The description of the discriminant locus of this elliptic fibration is given in detail. Moreover, the concrete description of the discriminant locus and the complete classification of singular fibres of the elliptic fibration are obtained according to Miranda's theory of elliptic threefolds after suitable modifications of the base and total spaces. Furthermore, the monodromy of the elliptic fibration is described.