Timeline for Is the Euler characteristic a birational invariant
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2021 at 22:35 | comment | added | Dan Petersen | @rmdmc89 I want to assume both $X$ and $Y$ smooth (and proper), for Hodge symmetry and $\Omega^p$ being locally free. | |
| Jun 10, 2021 at 20:28 | comment | added | rmdmc89 | The variety $Y$ in the birational map $X\to Y$ is not necessarily smooth, right? | |
| May 26, 2010 at 5:53 | comment | added | Torsten Ekedahl | Hodge symmetry also follows from the strong Lefschetz theorem for Hodge cohomology and Serre duality. The strong Lefschetz theorem for Hodge cohomology follows, I believe, from the strong Lefschetz theorem for étale cohomology and $p$-adic Hodge theory. Hence there should be an algebraic, though very involved, proof. (Though using a $p$-adic Lefschetz principle, instead of a complex one.) | |
| May 25, 2010 at 21:45 | comment | added | Ravi Vakil | This argument works for any subfield of the complex numbers as well of course. And it extends to any field of characteristic 0 by a Lefschetz principle argument (although as always there is a lot hidden in that statement). | |
| May 25, 2010 at 21:25 | history | answered | Dan Petersen | CC BY-SA 2.5 |