Picard theorems for Keller mappings in dimension two and the phantom curve

Research output: Contribution to journalArticle

Abstract

Let F = (P, Q) ∈ C[X, Y ] 2 be a polynomial mapping over the complex field C. Suppose that det JF (X, Y ) := ∂P ∂X ∂Q ∂Y − ∂P ∂Y ∂Q ∂X = a ∈ C ×. A mapping that satisfies the assumptions above is called a Keller mapping. In this paper we estimate the size of the co-image of F. We give a sufficient condition for surjectivity of Keller mappings in terms of its Phantom curve. This curve is closely related to the asymptotic variety
of F.
Original languageEnglish GB
JournalarXiv preprint
StatePublished - 2013

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