Timeline for No base-point free linear systems on linearly equivalent curves
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2017 at 7:31 | vote | accept | user52991 | ||
| Mar 31, 2017 at 10:12 | answer | added | Jason Starr | timeline score: 1 | |
| Mar 30, 2017 at 18:36 | comment | added | Jason Starr | ... for $e\geq 2$! | |
| Mar 30, 2017 at 7:55 | comment | added | Jason Starr | That can happen for many reasons. It might be that $|L|_s$ is a single point parameterizing a single curve $C$, and $G^r_d(C)$ also happens to be a single point. Here is a different example. Let $f:X\to \mathbb{CP}^2$ be a double cover that is simply branched over a plane curve of degree $2e$. Then $L=f^*\mathcal{O}(1)$ is ample and base point free. However, every $C\in |L|_s$ is hyperelliptic of genus $g=e-1$. Thus, for every $r\geq 1$, for every odd $d$ with $3\leq d\leq 2e-3$, every $(A,V)$ has nonempty base locus. | |
| Mar 30, 2017 at 7:14 | history | asked | user52991 | CC BY-SA 3.0 |