# Degenerations of Gushel-Mukai fourfolds, with a view towards irrationality proofs

## TL;DR

This paper investigates specific degenerations of Gushel-Mukai fourfolds to understand their irrationality, ultimately proving that certain natural degenerations do not exist, impacting approaches to irrationality proofs.

## Contribution

It introduces the concept of tame degenerations of Gushel-Mukai fourfolds and proves their non-existence, influencing methods for irrationality proofs.

## Key findings

- No tame degenerations of Gushel-Mukai fourfolds exist.
- Implications for degeneration-based irrationality proofs.
- Clarifies limitations of certain degeneration approaches.

## Abstract

We study a certain class of degenerations of Gushel-Mukai fourfolds as conic bundles, which we call tame degenerations and which are natural if one wants to prove that very general Gushel-Mukai fourfolds are irrational using the degeneration method due to Voisin, Colliot-Th\'{e}l\`{e}ne-Pirutka, Totaro et al. However, we prove that no such tame degenerations do exist.