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2. Pictures of Ramification
Each point of a parameterized plane curve has some ramification
(0,a,b).
Most points are unramified, with
(0,a,b)=(0,1,2).
Other points are called ramified.
We display pictures of ramified points, for small values of the ramification.
| (0,1,3) |
 |
| 1 |
| (s,s3) |
|
| (0,1,4) |
 |
| 2 |
| (s,s4) |
|
| (0,1,5) |
 |
| 3 |
| (s,s5) |
|
| (0,1,6) |
 |
| 4 |
| (s,s6) |
|
| (0,2,3) |
 |
| 11 |
| (s2,s3) |
|
| (0,2,4) |
 |
| 21 |
| (s2,s4) |
|
| (0,2,5) |
 |
| 31 |
| (s2,s5) |
|
| (0,2,6) |
 |
| 41 |
| (s2,s6) |
|
|
| (0,3,4) |
 |
| 22 |
| (s3,s4) |
|
| (0,3,5) |
 |
| 32 |
| (s3,s5) |
|
| (0,3,6) |
 |
| 42 |
| (s3,s6) |
|
| |
| (0,4,5) |
 |
| 33 |
| (s4,s5) |
|
| (0,4,6) |
 |
| 43 |
| (s4,s6) |
|
The `point' in the ramifications (0,3,4) and
(0,5,6) is an artifact of the scaling in the
picture. Those are smooth points in the
image curves.
| |
| (0,5,6) |
 |
| 44 |
| (s5,s6) |
|
Previous: 1.iii. Maximally Inflected Curves
Next: 3. Maximally Inflected Cubics
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