Automorphism groups of Calabi-Yau manifolds of Picard number two

By Keiji Oguiso. 2012

66 citations recorded by the source corpus.

We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\"ahler manifolds and birational automorphism groups, as we shall see. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation together with exsistence of rational curve, expected by the cone conjecture, for a Calabi-Yau threefold of Picard number two,

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/05f25ccea40f9e47abb89f4f3b3083e6f1ef7acc

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In Geometry and Topology

1. Tuyen T. T. Truong
2. Keiji Oguiso
3. D. Huybrechts
4. E. Markman
5. Nguyen-Bac Dang

In Mathematical Physics

1. Tuyen T. T. Truong
2. Keiji Oguiso
3. Nguyen-Bac Dang
4. D. Huybrechts

Citations in the corpus

• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy (2013, background): “ich structure in the complex dynamical view. We remark that also for CalabiYau manifolds, it seems much harder to construct biregular automorphisms compared with birational selfmaps (See for instance [Og12], [CO12]). On the other hand, our new manifold Y seems so far caught no attention. Now we stat”