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.

18 pages, 1 figure. v2 added proof that b_3 can also be taken arbitrarily large

References in corpus (4)

• Telescopic actions
• Geography of symplectic 4- and 6-manifolds
• Simply Connected Symplectic Calabi-Yau 6-Manifolds
• Coisotropic Luttinger surgery and some new symplectic 6-manifolds with vanishing canonical class

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• Kodaira Dimension in Low Dimensional Topology
• Geography of symplectic 4- and 6-manifolds
• Finite group actions on symplectic Calabi-Yau $4$-manifolds with $b_1>0$
• A report on the hypersymplectic flow
• The telescopic construction; a microsurvey