Timeline for Question on K3 Surface
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2012 at 18:50 | comment | added | Tony Pantev | @alex24: You should accept Remke's answer. It correctly and completely answers your question. | |
| Jun 10, 2012 at 18:43 | comment | added | Tony Pantev | As Remke Kloosterman points out - I got my Hurwitz formula wrong. To get the canonical class of the double cover to be trivial, you need to take a branch divisor that is in the twice the anticanonical linear system of the rational elliptic surface. So you simply need to take two smooth fibers as your branch divisor. This gives a smooth K3. It is the fiber product of the rational elliptic surface and a $\mathbb{P}^{1}$ doubly covering your original $\mathbb{P}^{1}$ with branching at the two points over which the two smooth fibers sit. | |
| Jun 10, 2012 at 6:52 | comment | added | user24328 | let say we don't assume K3 is smooth | |
| Jun 10, 2012 at 4:55 | history | answered | Tony Pantev | CC BY-SA 3.0 |