Pull-back of currents by meromorphic maps
摘要
Let X and Y be compact Khler manifolds, and let f : X Y be a dominant meromorphic map.Based upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator f for currents of bidegrees (p, p) of finite order on Y (and thus for any current, since Y is compact).This operator has good properties as may be expected.Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can be readily extended to the case of meromorphic correspondences.We give an example of a meromorphic map f and two nonzero positive closed currents T 1 , T 2 for which f (T 1 ) = -T 2 .We use Siu's decomposition to help further study on pulling back positive closed currents.Many applications on finding invariant currents are given. Rsum (Pull-back de courants par des applications mromorphes)Soient X et Y des varits khlriennes compactes, et f : X Y une application mromorphe dominante.En nous basant sur un thorme de rgularisation de Dinh et Sibony pour des courants DSH, nous dfinissons un oprateur pullback f pour les courants de bidegr (p, p) d'ordre fini sur Y (et donc pour tout courant, puisque Y est compact.Cet oprateur a des bonnes proprits, comme attendu.Notre dfinition et nos rsultats sont compatibles avec ceux des travaux prcdents de Meo, Russakovskii et