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The expanding zoo of Calabi-Yau threefolds. (English) Zbl 1234.81110
Summary: This is a short review of recent constructions of new Calabi-Yau threefolds with small Hodge numbers and/or nontrivial fundamental group, which are of particular interest for model building in the context of heterotic string theory. The two main tools are topological transitions and taking quotients by actions of discrete groups. Both of these techniques can produce new manifolds from existing ones, and they have been used to bring many new specimens to the previously sparse corner of the Calabi-Yau zoo, where both Hodge numbers are small. Two new manifolds are also obtained here from hyperconifold transitions, including the first example with fundamental group $$S_3$$, the smallest non-Abelian group.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14F35 Homotopy theory and fundamental groups in algebraic geometry 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
##### MathOverflow Questions:
A Calabi-Yau manifold with finite simple fundamental group?
##### Software:
Mathematica; SINGULAR; STRINGVACUA
Full Text:
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