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Abstract

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.