Finite quotients of three-dimensional complex tori
Annales de l'Institut Fourier, Volume 70 (2020) no. 2, pp. 881-914.

We provide a characterization of quotients of three-dimensional complex tori by finite groups that act freely in codimension one via a vanishing condition on the first and second orbifold Chern class. We also treat the case of free action in codimension two, using instead the “birational” second Chern class, as we call it.

Both notions of Chern classes are introduced here in the setting of compact complex spaces with klt singularities. In such generality, this topic has not been treated in the literature up to now. We also discuss the relation of our definitions to the classical Schwartz–MacPherson Chern classes.

Nous fournissons une caractérisation des quotients des tores complexes de dimension trois par l’action libre en codimension un d’un groupe fini, par une condition d’annulation de la première et deuxième classe de Chern orbifolde. Nous traitons aussi le cas des actions libres en codimension deux, utilisant la deuxième classe de Chern « birationelle », comme nous l’appelons, au lieu de la classe de Chern orbifolde.

Toutes les deux notions des classes de Chern sont introduites ici dans le cadre des espaces complexes compacts avec des singularités klt. Dans cette généralité, le sujet n’a pas été traité dans la littérature jusqu’à maintenant. Nous discutons aussi le rapport de notre définition aux classes de Chern classiques de Schwartz–MacPherson.

Received: 2018-06-07
Accepted: 2019-03-12
Published online: 2020-05-28
DOI: https://doi.org/10.5802/aif.3326
Classification: 32J27,  32S20,  53C55,  14E30
Keywords: Complex tori, torus quotients, vanishing Chern classes, second orbifold Chern class, Minimal Model Program, klt singularities
@article{AIF_2020__70_2_881_0,
     author = {Graf, Patrick and Kirschner, Tim},
     title = {Finite quotients of three-dimensional complex tori},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {70},
     number = {2},
     year = {2020},
     pages = {881-914},
     doi = {10.5802/aif.3326},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2020__70_2_881_0/}
}
Graf, Patrick; Kirschner, Tim. Finite quotients of three-dimensional complex tori. Annales de l'Institut Fourier, Volume 70 (2020) no. 2, pp. 881-914. doi : 10.5802/aif.3326. https://aif.centre-mersenne.org/item/AIF_2020__70_2_881_0/

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