Timeline for Kernels of surjections from a vector bundle to a reflexive sheaf
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2020 at 23:50 | comment | added | user127776 | As an answer to the question I asked above. The converse is not true i.e. if a reflexive sheaf is a vector bundle on the complement of a codimension 4 subvariety, it doesn't need to be locally 3-syzygy sheaf. I figured this out through an unexpected contradiction, there might be an easier way of showing it. | |
| Dec 23, 2020 at 5:16 | comment | added | Sasha | I learnt this stuff from the book of Okonek-Schneider-Spindler. | |
| Dec 23, 2020 at 5:00 | comment | added | R. van Dobben de Bruyn | Ah, can't you just prove that the same way as Tag 03BN? I think the point is that when you localise to a point of codimension $\leq 3$, you get a maximal Cohen–Macaulay module (see Tag 00NF), which is free by Tag 00NT. | |
| Dec 23, 2020 at 4:51 | comment | added | user127776 | I meant is the following statement true? "A reflexive sheaf is in my class iff it is a vector bundle on the complement of a closed subvariety of codimension 4" | |
| Dec 23, 2020 at 4:49 | comment | added | R. van Dobben de Bruyn | The case $m=1$ (torsion-free) is Tag 0AUU, and then $m=2$ follows from that and Tag 0AV2, and $m=3$ is your class by definition. | |
| Dec 23, 2020 at 4:42 | comment | added | user127776 | Is there a reference that proves this? Is this still true of the base field is not algebraically closed? | |
| Dec 23, 2020 at 4:41 | vote | accept | user127776 | ||
| Dec 23, 2020 at 4:34 | history | answered | Sasha | CC BY-SA 4.0 |