Geometry & Topology
- Geom. Topol.
- Volume 22, Number 4 (2018), 2115-2144.
A family of compact complex and symplectic Calabi–Yau manifolds that are non-Kähler
We construct a family of –dimensional compact manifolds which are simultaneously diffeomorphic to complex Calabi–Yau manifolds and symplectic Calabi–Yau manifolds. They have fundamental groups , their odd-degree Betti numbers are even, they satisfy the hard Lefschetz property, and their real homotopy types are formal. However, is never homotopy equivalent to a compact Kähler manifold for any topological space . The main ingredient to show the non-Kählerness is a structure theorem of cohomology jump loci due to the second author.
Geom. Topol., Volume 22, Number 4 (2018), 2115-2144.
Received: 17 June 2016
Revised: 15 April 2017
Accepted: 15 June 2017
First available in Project Euclid: 13 April 2018
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Qin, Lizhen; Wang, Botong. A family of compact complex and symplectic Calabi–Yau manifolds that are non-Kähler. Geom. Topol. 22 (2018), no. 4, 2115--2144. doi:10.2140/gt.2018.22.2115. https://projecteuclid.org/euclid.gt/1523584818