The diversity of symplectic Calabi-Yau six-manifolds
Abstract
Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these examples are not diffeomorphic to Kähler manifolds with c_1 = 0. The construction begins with a certain orientable four-dimensional hyperbolic orbifold assembled from right-angled 120-cells. The twistor space of the hyperbolic orbifold is a symplectic Calabi-Yau orbifold; a crepant resolution of this last orbifold produces a smooth symplectic manifold with the required properties.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.5944
- arXiv:
- arXiv:1108.5944
- Bibcode:
- 2011arXiv1108.5944F
- Keywords:
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- Mathematics - Symplectic Geometry;
- Mathematics - Differential Geometry;
- 53D05
- E-Print:
- 18 pages, 1 figure. v2 added proof that b_3 can also be taken arbitrarily large