A note on embeddings of projective spaces


Let \textbf{k} and \textbf{K} be commutative fields, and l,m integers with l ≥ 1, m ≥ 2. Suppose that there exists an embedding \psi of PG(m + l,\textbf{k}) to PG(m,\textbf{K}), then we have r = dim_{\textbf{k}}\textbf{K} ≥ 4 and m ≥ ≤ft [{3l}\over{r-3}\right] - 1. Conversely, there exists an embedding \psi of PG(l + m,\textbf{k}) to PG(m,\textbf{K}) if m ≥ ≤ft [{3l}\over{r-3}\right] - 1 and if (1) dim_{\textbf{k}}\textbf{K} = 4, or (2) dim_{\textbf{k}}\textbf{K} > 4 and \textbf{K} is a cyclic extension of \textbf{k} with some additional conditions on l and r.

DOI Code: 10.1285/i15900932v19n2p285

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