Timeline for smooth manifolds as real algebraic set (continued)

9 events

when toggle format	what		by	license	comment
Aug 31, 2013 at 16:30	history	edited	Alexandre Eremenko	CC BY-SA 3.0	error detected, new answer proposed
Aug 31, 2013 at 16:13	history	edited	Alexandre Eremenko	CC BY-SA 3.0	added 249 characters in body
Aug 31, 2013 at 16:07	comment	added	Alexandre Eremenko		@BS: you are right, sometimes the curves I proposed are singular.
Aug 31, 2013 at 10:43	comment	added	BS.		@Alexandre : there must be some misunderstanding here. Do you say that $CP^2$ contains a smooth complex curve of genus $2$ ? What is then its degree $d$ ? You can embed it in some rational surfaces, but not in $P^2$.
Aug 30, 2013 at 18:42	history	edited	Alexandre Eremenko	CC BY-SA 3.0	added 48 characters in body
Aug 30, 2013 at 18:40	comment	added	Alexandre Eremenko		@Jeremy Blanc: a smooth complex curve in $P^2$ is also a smooth real $2$-surface, and $P^2$ is a real algebraic variety if you forget the complex structure.
Aug 30, 2013 at 15:55	comment	added	Jérémy Blanc		And you get a variety defined over $\mathbb{C}$, not over $\mathbb{R}$.
Aug 30, 2013 at 13:29	comment	added	BS.		Only genuses $(d-1)(d-2)/2$, $d\ge 1$ are smoothly embeddable in $CP^2$. Your hyperelliptic affine model has singularities at infinity.
Aug 30, 2013 at 13:05	history	answered	Alexandre Eremenko	CC BY-SA 3.0