Polynomial maps with nilpotent Jacobians in dimension three
نویسندگان
چکیده
منابع مشابه
Nilpotent Jacobians in dimension three
In this paper we completely classify all polynomial maps of the form H = (u(x, y), v(x, y, z), h(u(x, y), v(x, y, z)) with JH nilpotent. AMS subject classification : 14R15, 14R10, 14E07.
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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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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.10.019