Hurwitz Number Fields

TL;DR

This paper investigates Hurwitz number fields arising from canonical covering maps in algebraic geometry, revealing examples that challenge existing mass heuristics by analyzing fibers over rational points.

Contribution

It provides new examples of Hurwitz number fields that contradict standard mass heuristics, enhancing understanding of their structure and distribution.

Findings

Identified Hurwitz number fields that defy mass heuristic predictions

Analyzed fibers of covering maps in algebraic geometry

Provided explicit examples of such number fields

Abstract

The canonical covering maps from Hurwitz varieties to configuration varieties are important in algebraic geometry. The scheme-theoretic fiber above a rational point is commonly connected, in which case it is the spectrum of a Hurwitz number field. We study many examples of such maps and their fibers, finding number fields whose existence contradicts standard mass heuristics.