The diversity of symplectic Calabi-Yau six-manifolds

Details The diversity of symplectic Calabi-Yau six-manifolds The diversity of symplectic Calabi-Yau six-manifolds

2011-08-30

arxiv.org/abs/1108.5944v2

Mathematics

Symplectic Geometry

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

Scientific paper

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 K\"ahler 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.

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