Timeline for Hilbert scheme of points on a surface as moduli space of semistable sheaves
Current License: CC BY-SA 3.0
6 events
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| Jul 25, 2022 at 3:50 | comment | added | Jack Huizenga | @euklid345 You need to be a bit careful here. For example, if F is a vector bundle then F and its double dual will have the same Chern classes. But if F has a simple singularity at a point (e.g. if there is an exact sequence $0\to F\to F^{**}\to O_p \to 0$) then F and its double dual will have different Chern classes. So if your moduli space parameterizes both vector bundles and sheaves with singularities then there is no flat "double dual" family. In the case here I don't see an issue though, because the double dual of the family should just be the constant family of $\mathcal{O}_X$'s. | |
| Jul 23, 2022 at 21:09 | comment | added | euklid345 | How do you know that this works in families? If F is a flat family of sheaves, why is the double dual of F still flat? | |
| Apr 4, 2013 at 20:55 | history | edited | Jack Huizenga | CC BY-SA 3.0 |
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| Apr 4, 2013 at 20:50 | vote | accept | HNuer | ||
| Apr 4, 2013 at 20:47 | history | edited | Jack Huizenga | CC BY-SA 3.0 |
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| Apr 4, 2013 at 20:42 | history | answered | Jack Huizenga | CC BY-SA 3.0 |