Timeline for Higher Weierstrass points on curves of genus 3
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2023 at 17:54 | comment | added | Lidia | Just two small comments. Those 108 points are exactly the 2-Weierstrass points of the quartic (counted with multiplicities), and the 84 counted with multiplicities, are the 2-Weierstrass which are not Weierstrass. Moreover, I think that the condition $h^0(C,dH-kp))>0$ is equivalent to the existence of a curve of degree 𝑑 with a contact of order $at$ $least$ $k$ with $C$ at $p$. Indeed, it can have contact 7 or 8. | |
| Mar 16, 2017 at 23:16 | comment | added | Ashvin Swaminathan | This is a great question/answer. Note further that the number $108$ includes the cases where the "sextactic" conic is singular. It turns out that the points at which the sextactic conic is singular are none other than the flexes of $C$ -- indeed, the doubled tangent line at a flex has contact of order $6$ with $C$ at the flex. There are precisely $3d(d-2) = 24$ such flexes on a genus $3$ plane curve, so the number of points at which the sextactic conic is smooth is only $84$. | |
| Feb 6, 2014 at 17:51 | vote | accept | Hugo Chapdelaine | ||
| Feb 6, 2014 at 6:32 | history | edited | abx | CC BY-SA 3.0 |
added 59 characters in body
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| Feb 6, 2014 at 6:17 | history | answered | abx | CC BY-SA 3.0 |