# Divisorial motivic zeta functions for marked stable curves

## TL;DR

This paper introduces a divisorial motivic zeta function for marked stable curves, extending Kapranov's function to singular and marked cases, proving its rationality and providing a dual graph formula.

## Contribution

It defines a new motivic zeta function for marked stable curves, generalizing previous work and establishing its rationality with a combinatorial formula.

## Key findings

- The divisorial motivic zeta function is rational.
- The zeta function coincides with Kapranov's for smooth, unmarked curves.
- A formula in terms of the dual graph of the curve is provided.

## Abstract

We define a divisorial motivic zeta function for stable curves with marked points which agrees with Kapranov's motivic zeta function when the curve is smooth and unmarked. We show that this zeta function is rational, and give a formula in terms of the dual graph of the curve.