Volume 22, issue 4 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A family of compact complex and symplectic Calabi–Yau manifolds that are non-Kähler

Lizhen Qin and Botong Wang

Geometry & Topology 22 (2018) 2115–2144
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.

Keywords
Kähler manifolds, Calabi-Yau manifolds
Mathematical Subject Classification 2010
Primary: 32J27, 53D05
References
Publication
Received: 17 June 2016
Revised: 15 April 2017
Accepted: 15 June 2017
Published: 5 April 2018
Proposed: Yasha Eliashberg
Seconded: Richard Thomas, Dan Abramovich
Authors
Lizhen Qin
Department of Mathematics
Nanjing University
Nanjing, Jiangsu
China
Botong Wang
Department of Mathematics
University of Wisconsin
Madison, WI
United States