Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian Conjecture
نویسندگان
چکیده
منابع مشابه
Some Properties of and Open Problems on Hessian Nilpotent Polynomials
In the recent work [BE1], [M], [Z1] and [Z2], the well-known Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed) inversion pairs. In this paper, we prove several results on HN polynomials, their (deformed) inversion pairs as well as on the associated symmetric polynomial or...
متن کاملSome Properties and Open Problems of Hessian Nilpotent Polynomials
In the recent progress [BE1], [M] and [Z2], the wellknown Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed) inversion pairs. In this paper, we prove several results on HN polynomials, their (deformed) inversion pairs as well as the associated symmetric polynomial or forma...
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Let k be a field of characteristic zero and F : k → k a polynomial map of the form F = x + H, where H is homogeneous of degree d ≥ 2. We show that the Jacobian Conjecture is true for such mappings. More precisely, we show that if JH is nilpotent there exists an invertible linear map T such that T−1HT = (0, h2(x1), h3(x1, x2)), where the hi are homogeneous of degree d. As a consequence of this r...
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We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).
متن کاملA Reduction of the Jacobian Conjecture to the Symmetric Case
The main result of this paper asserts that it suffices to prove the Jacobian Conjecture for all polynomial maps of the form x + H, where H is homogeneous (of degree 3) and JH is nilpotent and symmetric. Also a 6dimensional counterexample is given to a dependence problem posed by de Bondt and van den Essen (2003).
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تاریخ انتشار 2017