Given a field $K$, all polynomial maps
${\mathbb S}^{m_1}(K)\times\cdots\times{\mathbb S}^{m_k}(K)\to{\mathbb T}^n(K)$
of generalized tori over $K$ are studied. Furthermore, a full description of
holomorphic maps ${\mathbb C}^m\to{\mathbb C}^{n_1}\times\cdots\times{\mathbb
C}^{n_k}$ and ${\mathbb C}^{m_1}\times\cdots\times {\mathbb C}^{m_k}\to {\mathbb
C}^n$ which restrict to maps ${\mathbb T}^m\to{\mathbb
S}^{2n_1-1}\times\cdots\times{\mathbb S}^{2n_k-1}$ and ${\mathbb
S}^{2m_1-1}\times\cdots\times{\mathbb S}^{2m_k-1}\to{\mathbb T}^n$ respectively,
is presented.
Publié le : 2006-03-14
Classification:
holomorphic and polynomial maps,
sphere,
torus,
Zariski topology,
12D10,
14P25,
30C10,
32A10
@article{1148059339,
author = {Golasi\'nski, Marek and G\'omez Ruiz, Francisco},
title = {On maps of tori},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {12},
number = {5},
year = {2006},
pages = { 139-148},
language = {en},
url = {http://dml.mathdoc.fr/item/1148059339}
}
Golasiński, Marek; Gómez Ruiz, Francisco. On maps of tori. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp. 139-148. http://gdmltest.u-ga.fr/item/1148059339/