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Equidistribution of varieties for endomorphisms of projective spaces. (English) Zbl 1252.32025

Consider a non-invertible holomorphic endomorphism \(f\) of the \(k\)-dimensional complex projective space \(\mathbb{P}^k\) of degree \(d\geq2\) and an algebraic subvariety \(V\) of \(\mathbb{P}^k\) generic in the Zariski sense. The authors survey some results on the asymptotic equidistribution of the sequence \(f^{-n}(V)\) when \(n\) tends to infinity.

MSC:

32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
32A10 Holomorphic functions of several complex variables
32H30 Value distribution theory in higher dimensions
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