Timeline for Decomposition of $f^{*}T_X$ for a morphism $f:\mathbb{P}^1 \rightarrow X$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2012 at 7:48 | vote | accept | Luca Benzo | ||
| Jan 28, 2012 at 20:49 | answer | added | Sándor Kovács | timeline score: 6 | |
| Jan 28, 2012 at 14:42 | comment | added | Jason Starr | What you write is simply untrue. I suggest you look for "lines of type II" on cubic threefolds, e.g., as discussed in the paper of Clemens and Griffiths. Where in the literature does this "widely used fact" appear? | |
| Jan 28, 2012 at 10:41 | comment | added | Luca Benzo | Hi Damian, set-theoretically this is just the set of points $x \in X$ such that there exists a deformation of the curve $C \doteq f(\mathbb{P}^1)$ passing through $x$. I used the word "locus" cause I didn't try to prove that it is a (closed) subvariety in $X$, although this should be true (there a similar exercise in Debarre's book Higher dimensional algebraic geometry). | |
| Jan 28, 2012 at 10:20 | comment | added | Damian Rössler | @Luca Benzo. This is interesting. Could you explain in more detail what you mean by "the sublocus of $X$ swept out by deformations of $f$" ? | |
| Jan 28, 2012 at 10:15 | comment | added | Martin Brandenburg | Offtopic: The classification of vector bundles on the projective line was only rediscovered by Grothendieck. Dedekind-Weber already found it in 1892. | |
| Jan 28, 2012 at 9:58 | history | asked | Luca Benzo | CC BY-SA 3.0 |