Maximum likelihood degree of surjective rational maps

TL;DR

This paper introduces a numerical invariant called the ML degree for surjective rational maps on projective space and provides a formula to compute it using a specific vector bundle.

Contribution

It defines the ML degree for surjective rational maps and derives a formula to compute it via a naturally associated vector bundle.

Findings

ML degree is computable via the vector bundle $E_f$

Provides a new invariant for classifying surjective rational maps

Establishes a connection between algebraic geometry and vector bundle theory

Abstract

With any \emph{surjective rational map} $f: \mathbb{P}^n \dashrightarrow \mathbb{P}^n$ of the projective space we associate a numerical invariant (\emph{ML degree}) and compute it in terms of a naturally defined vector bundle $E_f \longrightarrow \mathbb{P}^n$.