Équidistribution vers le courant de Green

Frédéric Protin¹

¹ INSA Toulouse, Département GMM 135 Avenue de Rangueil 31400 Toulouse, France

Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 201-218

Résumé

We establish an equidistribution result for the pull-back of a $(1,1)$-closed positive current in $\mathbb {C}^2$ by a proper polynomial map of small topological degree. We also study convergence at infinity on good compactifications of $\mathbb {C}^2$. We make use of a lemma that enables us to control the blow-up of some integrals in the neighborhood of a big logarithmic singularity of a plurisubharmonic function. Finally, we discuss the importance of the properness hypothesis, and we give some results in the case where this hypothesis is omitted.

Détail

DOI : 10.4064/ap115-3-1

Mots-clés : establish equidistribution result pull back closed positive current mathbb proper polynomial map small topological degree study convergence infinity compactifications mathbb make lemma enables control blow up integrals neighborhood logarithmic singularity plurisubharmonic function finally discuss importance properness hypothesis results where hypothesis omitted