Differential conditions to verify the Jacobian Conjecture
نویسندگان
چکیده
منابع مشابه
On the Jacobian Conjecture
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k . Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given ...
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The paper is devoted to the proof of equivalence of Jacobian and Dixmier conjectures. We show that 2n-dimensional Jacobian conjecture implies Dixmier conjecture for Wn. The proof uses “antiquantization”: positive characteristics and Poisson brackets on the center of Weyl algebra in characteristic p. 2000 Math. Subj. Class. 16S32, 16S80, 14R15.
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The Jacobian Conjecture is a long-standing open problem in algebraic geometry. Though the problem is inherently algebraic, it crops up in fields throughout mathematics including perturbation theory, quantum field theory and combinatorics. This thesis is a unified treatment of the combinatorial approaches toward resolving the conjecture, particularly investigating the work done by Wright and Sin...
متن کاملOne Approach to the Jacobian Conjecture
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k. Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given b...
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In this paper we give a survey of various recent results obtained by the authors in the study of the Jacobian Conjecture. It is shown that it suffices to investigate the conjecture for polynomial maps of the form x+H with JH nilpotent and symmetric (and one may even assume that H is homogeneous of degree 3). Furthermore it is shown that for such maps the Jacobian Conjecture is true if n ≤ 4 and...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1992
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-57-3-253-263