Timeline for Symmetric powers for a short exact sequence of vector bundles
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 20 at 17:59 | comment | added | Jason Starr | It is much earlier than Hartshorne (of course). It should also be in Borel-Serre, for instance. | |
| Sep 20 at 17:41 | comment | added | Yellow Pig | @R.vanDobbendeBruyn Thank you very much! Is the filtration in the solution to that exercise given by the images of ${\rm Sym}^i A \otimes {\rm Sym}^{k-i} B$ in ${\rm Sym}^k B$? | |
| Sep 20 at 16:57 | comment | added | R. van Dobben de Bruyn | The first statement follows from Hartshorne, Exercise II.5.16(c), which constructs a filtration on $\operatorname{Sym}^k B$ whose associated graded is $\bigoplus_{i=0}^k \operatorname{Sym}^i A \otimes \operatorname{Sym}^{k-i} C$. | |
| Sep 20 at 16:44 | comment | added | Z. M | Yes. It is probably due to Dold, but reviewed in Section 3 of [Barwick–Glasman–Mathew–Nikolaus, K-theory and polynomial functors]. | |
| Sep 20 at 16:30 | history | edited | Yellow Pig | CC BY-SA 4.0 |
added 78 characters in body; edited title
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| Sep 20 at 16:23 | history | asked | Yellow Pig | CC BY-SA 4.0 |