Holomorphic linking numbers, ABC Massey products, and Calabi-Yau 3-folds

2025/12/01 by Lucía Martín‐Merchán, Martín-Merchán, Lucía, Jonas Stelzig +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2512.02187

openalex publication_date 2025/12/01 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

Abstract

On compact Kähler manifolds, we relate ABC Massey products arising from complex analytic cycles to holomorphic linking numbers. This enables us to construct a family of simply connected projective 3-folds with trivial canonical bundle, equipped with a non-vanishing ABC Massey product.

Citations

• Nontrivial Massey products on compact Kähler manifolds
• Bigraded notions of formality and Aeppli-Bott-Chern-Massey products
• On fibrations with formal elliptic fibers

Related

• Calabi--Yau 3-folds from projective joins of del Pezzo manifolds
• Nontrivial Massey products on compact Kähler manifolds
• Constructions and deformations of Calabi--Yau 3-folds in codimension 4
• Examples of non-formal closed (k-1)-connected manifolds of dimensions 4k-1 and more
• Complex Counterpart of Chern-Simons-Witten Theory and Holomorphic Linking