Note on the candidate counter-example in the cancellation problem for affine spaces posed by Arno Van den Essen

Autor: Oda, Sususu

We have proved the following Problem:{\it Let $R$ be a $\mathbb{C}$-affine domain, let $T$ be an element in $R \setminus \mathbb{C}$ and let $i : \mathbb{C}[T] \hookrightarrow R$ be the inclusion. Assume that $R/TR \cong_{\mathbb{C}} \mathbb{C}^{[n-1

Externí odkaz: http://arxiv.org/abs/1201.4198

Arno van den Essen: An Amazing Conjecture

Autor: Richard J. Lipton, Kenneth W. Regan

Publikováno v: People, Problems, and Proofs ISBN: 9783642414213

This chapter outlines a survey paper by van den Essen on the Jacobian Conjecture, which is on Stephen Smale’s short list of important problems besides the Millennium Prize ones. A new link discovered by Wenhua Zhao and broadened by van den Essen su

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::577d49f1bb4a6858724a3fa501919927
https://doi.org/10.1007/978-3-642-41422-0_7

Arno van den Essen: An Amazing Conjecture.

Autor: Lipton, Richard J., Regan, Kenneth W.

Publikováno v: People, Problems & Proofs; 2013, p45-50, 6p

Mathieu–Zhao Spaces

Autor: Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 113-177
Frontiers in Mathematics ISBN: 9783030605339

Throughout this section k denotes an algebraically closed field of characteristic zero. But, as the reader can check, most of the calculations done after Corollary 5.1.3 work equally well if k is just a commutative \(\mathbb Q\)-algebra.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb84c2cafe49c42c8e4360dcfa9d5540
https://repository.ubn.ru.nl/handle/2066/234048

The Jacobian Conjecture: New Equivalences

Autor: Arno van den Essen, Anthony J. Crachiola, Shigeru Kuroda

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 91-111
Frontiers in Mathematics ISBN: 9783030605339

As we have seen in van den Essen (Polynomial Automorphisms and the Jacobian Conjecture, Prog. Math., vol. 190, Birkhauser Verlag, Basel, 2000), there are various equivalent formulations of the Jacobian Conjecture. The aim of this chapter is to give f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f847404ea896d4dc05a47606e9d7e737
https://repository.ubn.ru.nl/handle/2066/234071