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The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show that how it leads to another fascinating and elusive assertion that we here dub the Factorial Conjecture. Various cases of the Factorial Conjecture are proved.
In this paper we give explicit factorizations which demonstrate the stable tameness of all polynomial automorphisms arising from a recent construction of Hubbers and van den Essen. This is accomplished by two different factorizations of such an automorphism by triangular automorphisms, one which is concise but requires a large number of additional dimensions, and one which is more intricate but requires...
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