Simply Connected Symplectic Calabi-Yau 6-Manifolds

2011/07/13 by Anar Akhmedov, Akhmedov, Anar
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1107.2623

openalex publication_date 2011/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T⁴. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group \Z. In this paper, we also produce the first examples of simply connected symplectic Calabi-Yau and non-Calabi-Yau 6-manifolds via coisotropic Luttinger surgery.

Citations

• Luttinger surgery and Kodaira dimension

Related

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• Symplectic analog of Calabi's conjecture for Calabi--Yau threefolds
• A Cheng-Yau type estimate for the symplectic Calabi-Yau equation
• Strictly nearly Kahler 6-manifolds are not compatible with symplectic forms
• Constructions of small symplectic 4-manifolds using Luttinger surgery