The diversity of symplectic calabi-yau 6-manifolds

TY - JOUR

T1 - The diversity of symplectic calabi-yau 6-manifolds

AU - Fine, Joel

AU - Panov, Dmitri

PY - 2013/9

Y1 - 2013/9

N2 - Given an integer b and a finitely presented group G, we produce a compact symplectic 6-manifold with c1 = 0, b2 > b, b3 > b and pi = G. In the simply connected case, we can also arrange for b3 = 0; in particular, these examples are not diffeomorphic to Kähler manifolds with c1 = 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.

AB - Given an integer b and a finitely presented group G, we produce a compact symplectic 6-manifold with c1 = 0, b2 > b, b3 > b and pi = G. In the simply connected case, we can also arrange for b3 = 0; in particular, these examples are not diffeomorphic to Kähler manifolds with c1 = 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.

UR - http://www.scopus.com/inward/record.url?scp=84883419451&partnerID=8YFLogxK

U2 - 10.1112/jtopol/jtt011

DO - 10.1112/jtopol/jtt011

M3 - Article

AN - SCOPUS:84883419451

SN - 1753-8416

VL - 6

SP - 644

EP - 658

JO - Journal of Topology

JF - Journal of Topology

IS - 3

ER -