On maps of tori

Abstract

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.