On the geometry of bifurcation currents for quadratic rational maps

TL;DR

This paper studies the behavior of bifurcation currents at infinity in the moduli space of quadratic rational maps, extending the current to a projective space and analyzing its properties.

Contribution

It introduces an extension of the bifurcation current to a compactified moduli space and computes its Lelong numbers and self-intersection, advancing understanding of bifurcation geometry.

Findings

Extended bifurcation current to a projective space.

Computed Lelong numbers of the extended current.

Analyzed self-intersection properties of the current.

Abstract

We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then compute the Lelong numbers and the self-intersection of the extended current.