Feuilleter
no. 2
Rigid currents in birational geometry
[Courants rigides en géométrie birationnelle]
Vladimir Lazić1 ; Zhixin Xie2
1Fachrichtung Mathematik, Campus, Gebäude E2.4, Universität des Saarlandes, 66123 Saarbrücken, Germany
2Institut Élie Cartan de Lorraine, Université de Lorraine, 54506 Nancy, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 437-457

A rigid current on a compact complex manifold is a closed positive current whose cohomology class contains only one closed positive current. Rigid currents occur in complex dynamics, algebraic and differential geometry. The goals of the present paper are: (a) to give a systematic treatment of rigid currents, (b) to demonstrate how they appear within the Minimal Model Program, and (c) to give many new examples of rigid currents.

Un courant rigide sur une variété complexe compacte est un courant positif fermé dont la classe de cohomologie ne contient qu’un seul courant positif fermé. Les courants rigides apparaissent dans la dynamique complexe, la géométrie algébrique et la géométrie différentielle. Les objectifs de cet article sont les suivants : (a) donner une méthode systématique pour étudier les courants rigides, (b) montrer comment ils apparaissent dans le Programme du Modèle Minimal, et (c) donner de nombreux exemples de courants rigides.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1852
Classification : 14E30, 32U40, 32J25
Keywords: rigid currents, currents with minimal singularities, Minimal Model Program
Mots-clés : courants rigides, courants avec singularités minimales, Programme du Modèle Minimal

Vladimir Lazić  1   ; Zhixin Xie  2

1 Fachrichtung Mathematik, Campus, Gebäude E2.4, Universität des Saarlandes, 66123 Saarbrücken, Germany
2 Institut Élie Cartan de Lorraine, Université de Lorraine, 54506 Nancy, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Vladimir Lazić; Zhixin Xie. Rigid currents in birational geometry. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 437-457. doi: 10.5802/afst.1852
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