Quaternionic Veronese Embedding - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T08:38:13Z http://mathoverflow.net/feeds/question/57501 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/57501/quaternionic-veronese-embedding Quaternionic Veronese Embedding Darius Alexander 2011-03-05T21:15:13Z 2011-03-05T21:15:13Z <p>I know that the complex projective line $\mathbb{C}P^1$ can be embedded in the complex projective space $\mathbb{C}P^n$ (Veronese embedding). For example, $\mathbb{C}P^1\rightarrow \mathbb{C}P^3$ is given explicitly by $(z,w)\rightarrow(z^3,z^2w,zw^2,w^3)$ in homogenous coordinates.</p> <p>I was wondering if the same could be done with quaternionic projective spaces, i.e. is there a 'veronese type' embedding: $\mathbb{H}P^1\rightarrow\mathbb{H}P^n$ ??</p> <p>(I know that the non-comutativity of quaternions make the veronese map ill defined)</p>