Timeline for triviality of determinant sheaf
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2012 at 18:46 | comment | added | Gunnar Þór Magnússon | $c_1(F) = 0$ does not imply that $F$ is trivial: Consider an elliptic curve $E$. Set $X = E \times E$. Let $g : (x,y) \mapsto (x+1/2,-y)$ be an involution w/o fixed points on $X$. Then the canonical bundle of the quotient $Z = X / \langle g \rangle$ has zero first Chern class, but is not trivial since it has no non-zero sections. | |
| Aug 7, 2012 at 18:43 | comment | added | user25309 | I want to show that the determinant bundle is algebraically trivial, what can not be seen in cohomology. Even if one works over \mathbb{C}, I don't know how to prove that it is topologically trivial. I don't understand why the first Chern class should live in the cohomology with support in Supp(F). | |
| Aug 7, 2012 at 18:19 | history | answered | Youloush | CC BY-SA 3.0 |