Polynomial Automorphisms and the Jacobian Conjecture

نویسندگان

چکیده

This book deals with the development on polynomial rings in last two decades since publication of “Polynomial Automorphisms” by Arno van den Essen. It is written experts who themselves have been able to make a significant contribution these problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Polynomial Automorphisms and the Jacobian Conjecture

In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counter-examples, in all dimensions greater than two, to the Markus-Yamabe conjecture (Global asymptotic Jacobian conjecture). Résumé Dans ce papier nous pr...

متن کامل

Polynomial Retracts and the Jacobian Conjecture

Let K[x, y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra R of K[x, y] is called a retract if there is an idempotent homomorphism (a retraction, or projection) φ : K[x, y] → K[x, y] such that φ(K[x, y]) = R. The presence of other, equivalent, definitions of retracts provides several different methods of studying them, and brings together ideas from ...

متن کامل

Endomorphisms of Polynomial Rings ; the Jacobian Conjecture

The Jacobian Conjecture is established : If f1, · · · , fn be elements in a polynomial ring k[X1, · · · , Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1, · · · , fn] = k[X1, · · · , Xn]. 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 کامل

Inversion of polynomial species and jacobian conjecture

We consider the following problem in the theory of (virtual) species of structures: Given a polynomial species F such that its derivative dF equals 1, will its inverse w.r.t substitution F h?1i also be polynomial species? We shall see that this is in general not the case. From this result it follows that an analogue of the jacobian conjecture in the context of species does not hold.

متن کامل

Outer Automorphisms and the Jacobian

A graphs of rank n (homotopy equivalent to a wedge of n circles) without “separating edges” has a canonical n-dimensional compact C manifold thickening. This implies that the canonical homomorphism φ : Out(Fn) → GL(n,Z) is trivial in rational cohomology in the stable range answering a question raised in [6]. Another consequence of the construction is the existence of higher Reidemeister torsion...

متن کامل

ذخیره 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: Frontiers in mathematics

سال: 2021

ISSN: ['1660-8046', '1660-8054']

DOI: https://doi.org/10.1007/978-3-030-60535-3