# Resurgence numbers of fiber products of projective schemes

## TL;DR

This paper studies how the resurgence and asymptotic resurgence numbers behave for fiber products of projective schemes, revealing that while the asymptotic resurgence remains constant, the resurgence number can increase.

## Contribution

It provides new insights into the behavior of resurgence numbers under fiber products, highlighting differences between resurgence and asymptotic resurgence.

## Key findings

- Asymptotic resurgence remains unchanged under k-fold fiber products.
- Resurgence number can strictly increase with fiber products.
- Distinct behaviors of resurgence and asymptotic resurgence are demonstrated.

## Abstract

We investigate the resurgence and asymptotic resurgence numbers of fiber products of projective schemes. Particularly, we show that while the asymptotic resurgence number of the k-fold fiber product of a projective scheme remains unchanged, its resurgence number could strictly increase.