Automorphism groups of Calabi-Yau manifolds of Picard number 2

Oguiso, Keiji

doi:10.1090/S1056-3911-2014-00642-1

Automorphism groups of Calabi-Yau manifolds of Picard number $2$

Author: Keiji Oguiso
Journal: J. Algebraic Geom. 23 (2014), 775-795
DOI: https://doi.org/10.1090/S1056-3911-2014-00642-1
Published electronically: April 29, 2014
MathSciNet review: 3263669
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Abstract | References | Additional Information

Abstract: We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number $2$ is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperkähler 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 hyperkähler manifold of Picard number $2$. We will also discuss a similar conjectual relation together with the exsistence of a rational curve, expected by the cone conjecture, for a Calabi-Yau threefold of Picard number $2$.

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Additional Information

Keiji Oguiso
Affiliation: Department of Mathematics, Osaka University, Toyonaka 560-0043 Osaka, Japan; and Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Korea
Email: oguiso@math.sci.osaka-u.ac.jp

Received by editor(s): June 18, 2012
Received by editor(s) in revised form: March 6, 2013
Published electronically: April 29, 2014
Additional Notes: This work was supported by JSPS Gran-in-Aid (B) No. 22340009, JSPS Grant-in-Aid (S) No. 22224001, and by KIAS Scholar Program
Dedicated: Dedicated to Professor Yujiro Kawamata on the occasion of his sixtieth birthday
Article copyright: © Copyright 2014 University Press, Inc.