# A decomposition theorem for smoothable varieties with trivial canonical class

## TL;DR

This paper proves that certain smoothable complex projective varieties with trivial canonical class can be decomposed into a product of simpler varieties, including abelian, Calabi-Yau, and symplectic types, via a finite cover.

## Contribution

It establishes a decomposition theorem for smoothable varieties with trivial canonical class, extending the understanding of their structure in algebraic geometry.

## Key findings

- Existence of a finite cover decomposing the variety into product components.
- Decomposition includes abelian, Calabi-Yau, and symplectic analogues.
- Applicable to varieties smooth in codimension two with klt singularities.

## Abstract

In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, \'etale in codimension one, that decomposes as a product of an abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible symplectic varieties.