Holomorphic linking numbers, ABC Massey products, and Calabi-Yau 3-folds
Luc\'ia Mart\'in-Merch\'an, Jonas Stelzig
TL;DR
This paper explores the relationship between ABC Massey products and holomorphic linking numbers on compact Kähler manifolds, leading to the construction of specific Calabi-Yau 3-folds with notable algebraic properties.
Contribution
It establishes a connection between complex analytic cycles and holomorphic linking, and constructs new Calabi-Yau 3-folds with non-vanishing Massey products.
Findings
Relation between ABC Massey products and linking numbers
Construction of Calabi-Yau 3-folds with non-vanishing Massey products
Identification of simply connected projective 3-folds with trivial canonical bundle
Abstract
On compact K\"ahler 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.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics