Timeline for Horrocks Mumford surface and other surfaces in $\mathbb P^4$
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2011 at 9:29 | comment | added | inkspot | The HM bundle $E$ has $c_1=5H$ and $c_2=10H^2$ where $H$ is the class of a hyperplane, and is the only known indecomposable rank two bundle with these Chern classes. But then if $f:\mathbb P^4\to\mathbb P^4$ is not constant and $deg(f)>1$ the pullback $f^*E$ will also be indecomposable and have larger Chern classes. (And two even more trivial remarks: "The" in line 1 is questionable: there is a $3$-dimensional moduli space of these surfaces. They do not arise as the zero-section of a vector bundle on $\mathbb P^4$, but rather the zero-locus of a non-zero section of such a bundle.) | |
| Sep 21, 2011 at 7:00 | answer | added | Sasha | timeline score: 4 | |
| Sep 20, 2011 at 16:04 | history | asked | Nick | CC BY-SA 3.0 |