Review Article
The Expanding Zoo of Calabi-Yau Threefolds
Table 2
Manifolds with small Hodge numbers and .
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
This table complements the one in [2], and briefly describes the manifolds which have and nontrivial fundamental group discovered since that paper appeared in 2008. There should still be a number of other manifolds in this region, including quotients from [23] whose Hodge numbers have not yet been calculated, and manifolds obtained from known quotients by hyperconifold transitions [37], of which only a few have so far been written down explicitly. In the “Manifold” column, denotes the Calabi-Yau toric hypersurface associated to the 24-cell, discussed in [25] and Section 2.2.3, while refers to the manifold discussed in Section 2.2.2, and to that in Section 2.2.1. is the del Pezzo surface of degree . Multiple quotient groups indicate different quotients with the same Hodge numbers. denotes a singular member of a generically smooth family, while denotes a resolution of a singular variety . The column labelled by gives the fundamental group. For each manifold listed here there should also be a mirror, which is not listed. |