Timeline for Dual of slope semistable vector bundle on higher dimensional variety
Current License: CC BY-SA 4.0
4 events
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| Jul 11 at 13:02 | history | edited | Henri | CC BY-SA 4.0 |
typo
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| Jul 11 at 11:19 | comment | added | Will Sawin | @maxo For your second question, we work locally, and the local rings in codimension $1$ are discrete valuation rings (because $X$ is regular). Submodules of free modules over DVRs are free, and modules over DVRs are free unless they contain torsion, but torsion elements would contradict saturatedness. | |
| Jul 11 at 11:18 | comment | added | Will Sawin | @maxo "destabilizing" just means that $F$ contradicts the inequality which all subsheaves need to satisfy if $E$ is stable. This is the same sense it is used in "maximal destabilizing subsheaf". One could probably run the argument with a maximal destabilizing subsheaf in which case I guess one would check that this sheaf is already saturated. | |
| Jul 10 at 18:15 | history | answered | Will Sawin | CC BY-SA 4.0 |