Galois covers of Calabi-Yau manifolds

TL;DR

This paper investigates Galois rational maps between Calabi-Yau and Hyper-K"ahler manifolds, providing new insights into their birational geometry and Galois closures, with applications to classical examples.

Contribution

It offers novel results on the birational geometry and Galois closures of rational maps specifically between Calabi-Yau and Hyper-K"ahler manifolds.

Findings

Results on the birational geometry of Galois rational maps

Analysis of Galois closures in the context of Calabi-Yau manifolds

Applications to well-known examples of Calabi-Yau and Hyper-K"ahler varieties

Abstract

We study Galois rational maps between smooth projective varieties with trivial canonical bundle, with a particular interest in the case where the codomain is Hyper-K\"ahler. We obtain results about the birational geometry and the Galois closure of rational maps between Calabi-Yau manifolds. We apply these general results to a number of well-known examples.