Timeline for 3-secant lines of a projective curve
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2021 at 0:21 | answer | added | Will Sawin | timeline score: 4 | |
| Feb 18, 2021 at 0:06 | comment | added | Will Sawin | The expected dimension is $4-n$. This should be what you see for a sufficiently general curve $C$ - dimension $1$ if $n=3$, $0$ if $n=4$, and empty for $n>4$. | |
| Feb 17, 2021 at 23:14 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 27 characters in body
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| Feb 17, 2021 at 20:46 | comment | added | abx | The answer depends very much on the embedding. Assuming that $C$ is embedded by a complete linear system $\lvert L\rvert$, $S_3(C)=\varnothing$ is equivalent to $h^0(L(-D_3))=h^0(L)-3$ for all effective divisors $D_3$ of degree 3. This is the case in particular if $\deg(C)\geq 2g+2$; it is also true for the canonical embedding ($L=K$) if $C$ is not hyperelliptic or trigonal. | |
| Feb 17, 2021 at 20:10 | history | asked | user125056 | CC BY-SA 4.0 |