Stable properties under weakly geometrically flat maps
DOI:
https://doi.org/10.7146/math.scand.a-148979Abstract
In this note we show that a weakly geometrically flat map π:M→N between pure dimensional complex spaces has the local lifting property for cycles. From this result we also deduce that, under these hypotheses, several properties of M are transferred to N.
References
Barlet, D., and Magnússon, J., Complex analytic cycles I: Basic results on complex geometry and foundations for the study of cycles, Grundlehren der mathematischen Wissenschaften 356, Springer, Cham, 2019.
https://doi.org/10.1007/978-3-030-31163-6
Barlet, D., and Magnússon, J., Cycles analytiques complexe II: l'espace des cycles, Cours Spécialisés 27, Société Mathématique de France, Paris, 2020.
Greb, D., Kebekus, S., Kovacs, S. J., and Peternell T., Differential forms on log canonical spaces, Publ. Math. Inst. Hautes Études Sci. No. 114 (2011), 87–169. https://doi.org/10.1007/s10240-011-0036-0
Kebekus, S., and Schnell, C., Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities, J. Amer. Math. Soc. 34 (2021), no. 2, 315–368. https://doi.org/10.1090/jams/962
