Geometry & Topology

A family of compact complex and symplectic Calabi–Yau manifolds that are non-Kähler

Lizhen Qin and Botong Wang

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Abstract

We construct a family of 6 –dimensional compact manifolds M ( A ) 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, M ( A ) × Y is never homotopy equivalent to a compact Kähler manifold for any topological space Y . The main ingredient to show the non-Kählerness is a structure theorem of cohomology jump loci due to the second author.

Article information

Source
Geom. Topol., Volume 22, Number 4 (2018), 2115-2144.

Dates
Received: 17 June 2016
Revised: 15 April 2017
Accepted: 15 June 2017
First available in Project Euclid: 13 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.gt/1523584818

Digital Object Identifier
doi:10.2140/gt.2018.22.2115

Mathematical Reviews number (MathSciNet)
MR3784517

Zentralblatt MATH identifier
06864333

Subjects
Primary: 32J27: Compact Kähler manifolds: generalizations, classification 53D05: Symplectic manifolds, general

Keywords
Kähler manifolds Calabi-Yau manifolds

Citation

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


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