# A special Calabi-Yau degeneration with trivial monodromy

## TL;DR

This paper demonstrates that, unlike K3-surfaces, Calabi-Yau threefolds can have degenerations with trivial monodromy that do not extend to smooth families, challenging existing assumptions.

## Contribution

It provides a counterexample showing the failure of a known degeneration extension theorem for Calabi-Yau threefolds.

## Key findings

- Counterexample to the extension of trivial monodromy degenerations
- Shows the difference between K3-surfaces and Calabi-Yau threefolds
- Highlights limitations of existing degeneration theorems

## Abstract

A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds.