Timeline for Fixed Point Property in Algebraic Geometry
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2010 at 12:21 | comment | added | Frank | By the way Harris' exercise 1.25 is essentially Corollary 4.18 in Debarre's book 'Higher dimensional algebraic geometry'. | |
| Mar 16, 2010 at 21:01 | comment | added | AndreA | Torsten: could you elaborate more? And do you have any thought on the applicability of your idea to my related question mathoverflow.net/questions/18347/… ? | |
| Mar 16, 2010 at 20:49 | comment | added | Piotr Achinger | Torsten: thank you, your comment really answers my question! Perhaps it would be better to post it as an answer, so I could mark it green... | |
| Mar 16, 2010 at 20:14 | comment | added | Torsten Ekedahl | The exercise is no doubt referring to the higher cohomology of the structure sheaf. The holomorphic Lefschetz fixed point formula shows that if its higher cohomology vanishes then any endomorphism has fixed points. This also answers the question as even just the vanishing of $h^{0,p}$ for $p>0$ ensures the existence of a fixed point. | |
| Mar 16, 2010 at 19:49 | comment | added | Pete L. Clark | Are you talking about Homework 1.25? I find this confusing. It says that rationally connected varieties have no higher cohomology and that their Euler characteristic is 1. But the Euler characteristic of CP^n is n+1. | |
| Mar 16, 2010 at 19:27 | history | answered | Frank | CC BY-SA 2.5 |