Timeline for relative flatness and torsion freeness
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2010 at 7:00 | comment | added | kaddar | We have a partial answer to the first question: $f:X\rightarrow S$ proper and surjective morphisme of reduced complex with $X$ pure dimensional and $S$ irreducible. If $F$ is an $S$-flat coherent sheaf, we have the equivalence: a) There existe some point $s$ in $S$, for which $F_{s}$ is a torsion free $O_{X_{s}}$-module. b) $F$ is a torsion free $O_{X}$-coherent sheaf. The proof can be donne by intensive use of Siu-Trautman result on degeneracy set of coherent sheaf ... | |
| Oct 9, 2010 at 19:35 | comment | added | Sasha | Flat over what? | |
| Oct 8, 2010 at 16:41 | comment | added | kaddar | Dear Sasha, can you give me an example of torsion free sheaf on complex reduced pure dimensional space which are no flat ? | |
| Oct 8, 2010 at 10:59 | comment | added | Sasha | For the first question the answer is NO even for $S$ being a point! | |
| Oct 8, 2010 at 7:57 | history | asked | kaddar | CC BY-SA 2.5 |