Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups

Details Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups

2011-07-29

arxiv.org/abs/1107.5862v2

Mathematics

Algebraic Geometry

18pgaes, a few minor changes, including wrong signs in the formula in pages 3, 4 are corrected and argument in page 7 lines 4-

Scientific paper

We prove that the birational automorphism group of any Calabi-Yau manifold given by a generic hypersurface of multi-degree two in $({\mathbf P^1})^{n+1}$ is isomorphic to the universal Coxeter group of rank $n+1$ and satisfies the Morrison-Kawamata movable cone conjecture. Schr\"oer and I found a new series of Calabi-Yau manifolds of even dimension, namely, the universal covers of punctual Hilbert schemes of Enriques surfaces. We also prove that they admit a biregular action of the universal Coxeter group of rank 3 with positive entropy for generic Enriques surfaces.

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