@inbook{980ab41d0b2146fbb0b89af0e5c6bb9c,

title = "Quotients of Calabi–Yau varieties",

abstract = "Let X be a complex Calabi–Yau variety, that is, a complex projective variety with canonical singularities whose canonical class is numerically trivial. Let G be a finite group acting on X and consider the quotient variety X/G. The aim of this paper is to determine the place of X/G in the birational classification of varieties. That is, we determine the Kodaira dimension of X/G and decide when it is uniruled or rationally connected. If G acts without fixed points, then κ(X/G) = κ(X) = 0; thus the interesting case is when G has fixed points. We answer the above questions in terms of the action of the stabilizer subgroups near the fixed points. We give a rough classification of possible stabilizer groups which cause X/G to have Kodaira dimension −∞ or equivalently (as we show) to be uniruled. These stabilizers are closely related to unitary reflection groups.",

keywords = "Calabi–Yau, Rationally connected, Reflection group, Uniruled",

author = "J{\'a}nos Koll{\'a}r and Michael Larsen",

note = "Funding Information: Acknowledgments. We thank Ch. Hacon, S. Kov{\'a}cs, and C. Voisin for helpful comments and references and De-Qi Zhang for correcting an error in an earlier version of Theorem 3. Partial financial support to JK and ML was provided by the NSF under grant numbers DMS-0500198 and DMS-0354772.",

year = "2009",

doi = "10.1007/978-0-8176-4747-6_6",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "179--211",

booktitle = "Progress in Mathematics",

}