Timeline for Gonality and Clifford dimension of curves on a K3 surface
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2015 at 18:16 | vote | accept | gradstudent | ||
| Oct 29, 2015 at 18:16 | |||||
| Oct 23, 2015 at 19:09 | comment | added | gradstudent | Ah yes, but this does not happen for Kummer surfaces @dhy | |
| Oct 23, 2015 at 19:00 | comment | added | dhy | @poorna But that follows from Pic(X)=Z[L]; I think as long as that's true, it doesn't matter if C is generic in the linear system. | |
| Oct 23, 2015 at 18:36 | comment | added | gradstudent | @dhy, In the paper, Lazarsfeld assumes that every curve $C\in |L|$ is reduced and irreducible. | |
| Oct 19, 2015 at 18:59 | comment | added | dhy | Doesn't Lazarsfeld actually prove that any smooth curve in $|L|$ is Brill-Noether general (Corollary 1.4 in his paper)? | |
| Oct 19, 2015 at 10:30 | comment | added | abx | Unfortunately no -- a Kummer surface has a very high Picard number (>16). | |
| Oct 19, 2015 at 10:06 | comment | added | gradstudent | Thanks @abx! When $X$ is the Kummer surface associated to an abelian surface, then can this happen? That is the specific case I am looking at. Maybe I should edit the question. | |
| Oct 19, 2015 at 9:45 | history | answered | abx | CC BY-SA 3.0 |