Finite morphisms and Nash multiplicity sequences

TL;DR

This paper investigates the relationship between finite morphisms of algebraic varieties and their multiplicity loci, using arc spaces to understand how these features correspond under specific conditions.

Contribution

It introduces a method to analyze the link between multiplicity loci of varieties and their finite morphisms via arc spaces, under certain assumptions.

Findings

Established a connection between multiplicity loci and arc spaces.

Provided criteria to determine the link under specific assumptions.

Enhanced understanding of finite morphisms in algebraic geometry.

Abstract

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.