# Vanishing cycles under base change and the integral Hodge conjecture

## TL;DR

This paper investigates how vanishing cycles influence the integral Hodge conjecture, providing new counterexamples by analyzing their behavior under base change, notably involving hypersurfaces and Enriques surfaces.

## Contribution

It introduces a novel obstruction based on vanishing cycles to the integral Hodge conjecture and generalizes existing degeneration methods to produce new counterexamples.

## Key findings

- Constructed counterexamples involving hypersurfaces and Enriques surfaces
- Identified a new obstruction from vanishing cycles affecting the conjecture
- Extended degeneration techniques of Benoist-Ottem

## Abstract

In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such counter-example is the product of a very general hypersurface of odd dimension and an Enriques surface. Our approach generalizes the degeneration argument of Benoist-Ottem.