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Timeline for Hyperelliptic Curve [closed]

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S Dec 16, 2013 at 15:32 history unlocked CommunityBot
S Dec 16, 2013 at 15:32 history locked CommunityBot
S Dec 16, 2013 at 15:32 history closed Ricardo Andrade
Daniel Moskovich
j.c.
Stefan Kohl♦
Chris Godsil 		Not suitable for this site
Dec 16, 2013 at 15:10 comment added Jack Huizenga You can also embed the curve in a quadric: mathoverflow.net/questions/79546
Dec 16, 2013 at 13:59 review Close votes
Dec 16, 2013 at 15:32
Dec 16, 2013 at 13:56 comment added Joe Silverman Alternatively to working in a weighted projective space is to write your curve as two smooth affine curves that are glued together. (I think this is actually more standard than weighted projective spaces, but chacun a son gout.) Also, this question is likely to be closed, since it's really not research level, so it would be better on MathStackExchange. But don't feel that that's an insult or be discouraged, we all started by learning basic concepts.
Dec 16, 2013 at 13:05 comment added Daniel Loughran Exactly. The usual definition of a hyperelliptic curve is a smooth projective curve birational to a curve of the form $y^2 = f(x)$, where $f$ is separable. The equation you have written down is not smooth. To obtain the smooth projective model, one usually works in a weighted projective space.
Dec 16, 2013 at 12:58 review First posts
Dec 16, 2013 at 13:03
Dec 16, 2013 at 12:55 comment added Beginner2013 You mean the problem is that the curve is not smooth at [0:1:0]?
Dec 16, 2013 at 12:51 comment added Daniel Loughran This is a fairly standard exercise on hyperelliptic curves, it would be good for you to work it out yourself. The problem lies with your application of the adjunction formula.
Dec 16, 2013 at 12:42 history asked Beginner2013 CC BY-SA 3.0