dc.creatorAuffarth, Robert
dc.creatorArteche, Giancarlo
dc.date.accessioned2021-08-23T16:08:45Z
dc.date.available2021-08-23T16:08:45Z
dc.date.created2021-08-23T16:08:45Z
dc.date.issued2020
dc.identifierMathematische Zeitschrift (2020)
dc.identifier10.1007/s00209-021-02826-3
dc.identifierhttps://repositorio.uchile.cl/handle/2250/181388
dc.description.abstractLet T be a complex torus and G a finite group acting on T without translations such that T/G is smooth. Consider the subgroup F <= G generated by elements that have at least one fixed point. We prove that there exists a point x is an element of T fixed by the whole group F and that the quotient T/G is a fibration of products of projective spaces over an etale quotient of a complex torus (the etale quotient being Galois with group G/F). In particular, when G = F, we may assume that G fixes the origin. This is related to previous work by the authors, where the case of actions on abelian varieties fixing the originwas treated. Here, we generalize these results to complex tori and use them to reduce the problem of classifying smooth quotients of complex tori to the case of etale quotients. An ingredient of the proof of our fixed-point theorem is a result proving that in every irreducible complex reflection group there is an element which is not contained in any proper reflection subgroup and that Coxeter elements have this property for well-generated groups. This result is proved by Stephen Griffeth in an appendix.
dc.languageen
dc.publisherSpringer Heidelberg
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/cl/
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Chile
dc.sourceMathematische Zeitschrift
dc.subjectComplex tori
dc.subjectSmooth quotients
dc.subjectComplex reflection groups
dc.titleSmooth quotients of complex tori by finite groups
dc.typeArtículo de revista


Este ítem pertenece a la siguiente institución