Lefschetz numbers of iterates of the monodromy and truncated arcs

TL;DR

This paper links the Lefschetz number of monodromy iterates to the Euler characteristic of truncated arc spaces, providing a new geometric perspective on monodromy behavior in complex algebraic varieties.

Contribution

It introduces a novel expression for Lefschetz numbers of monodromy iterates using Euler characteristics of truncated arc spaces, bridging algebraic topology and algebraic geometry.

Findings

Lefschetz numbers are expressed via Euler characteristics of arc spaces

Provides a geometric interpretation of monodromy iterates

Establishes connections between monodromy and arc space topology

Abstract

We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs.