The Jacobian conjecture for symmetric Jacobian matrices
نویسندگان
چکیده
منابع مشابه
Nilpotent Symmetric Jacobian Matrices and the Jacobian Conjecture Ii
It is shown that the Jacobian Conjecture holds for all polynomial maps F : k → k of the form F = x + H , such that JH is nilpotent and symmetric, when n ≤ 4. If H is also homogeneous a similar result is proved for all n ≤ 5. Introduction Let F := (F1, . . . , Fn) : C → C be a polynomial map i.e. each Fi is a polynomial in n variables over C. Denote by JF := (i ∂xj )1≤i,j≤n, the Jacobian matrix ...
متن کاملOn 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 ...
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).
متن کاملOn Jacobian conjecture
Any endomorphism of Cn defined by n polynomials with everywhere non-vanishing Jacobian is an automorphism. The Jacobian conjecture originated fromKeller ([5]). Let F1, . . . , Fn ∈ C[x1, . . . , xn] be a set of n polynomials in n variables with n ≥ 1 such that the Jacobian of these polynomials is a nonzero constant. The Jacobian conjecture says that the subalgebra C[F1, . . . , Fn] of C[x1, . ....
متن کاملHesse and the Jacobian Conjecture
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2003.10.020