Although this article has a reasonable amount of content, I give it merely "start" class because it is so hard to understand. There is no separate lede, and the definition is hidden in a mess of historical and technical comments and theoretical "motivation" that makes sense only to someone already well-versed in the material. The entire opening text needs to be sectioned off and its structure justified: is it necessary to define the dual variety in this case-by-case manner? What exactly is "the theory" that was first put into good form for the complex numbers? What do all of these terms like "Albanese variety", "Jacobian variety", "principal polarization", etc. mean (they should be recalled in the article, together with the links)? The material on the dual isogeny for elliptic curves is currently disproportionate to the main article and threatens to choke it off entirely, when in fact it is just an example of an accessible special case, which should be made more evident.
Ryan Reich 15:39, 16 May 2007 (UTC)
