Galois covers of Calabi-Yau manifolds

2025/07/18 by Matteo Verni, Verni, Matteo
Mathematics · #14E05 #14E20 #14J42 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.14359

openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Kähler. 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.

Citations

• Lines, Twisted Cubics on Cubic Fourfolds, and the Monodromy of the Voisin Map
• Isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds
• Characteristic foliations -- a survey
• On the Boucksom-Zariski decomposition for irreducible symplectic varieties and bounded negativity
• The Deligne-Mostow list and special families of surfaces
• Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kähler varieties
• Twisted cubics on cubic fourfolds
• Enriques manifolds
• A computation of invariants of a rational self-map
• Characterization of Abelian Varieties

Related

• Hodge theory, algebraic cycles of hyper-Kähler manifolds
• Rational curves on fibered Calabi-Yau manifolds
• New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds
• Calabi-Yau fibrations, simple K-equivalence and mutations
• Calabi-Yau Varieties with Fibre Structures