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A sharp bound for the degree of proper monomial mappings between balls. (English) Zbl 1052.26016

In this interesting paper the authors prove the following theorem. Suppose that \(p\) is a polynomial in two real variables \((x,y)\) with real coefficients, such that \(p(x,y)=1\), if \(x+y=1\). Let \(N\) be the number of distinct monomials in \(p\), and let \(d\) be the degree of \(p\). Then \(d\leq 2N-3\) and this result is sharp. As a corollary, they show that if \(f\) is a proper holomorphic monomial mapping from the unit ball in \(\mathbb C^2\) to the unit ball in \(\mathbb C^N\), then the degree of \(f\) does not exceed \(2N-3\), and this result is sharp.

MSC:

26C05 Real polynomials: analytic properties, etc.
32B99 Local analytic geometry
11B83 Special sequences and polynomials
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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References:

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