Timeline for Examples of tilting objects that don't come from exceptional sequences
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2013 at 12:30 | comment | added | Sasha Pavlov | I'm sorry, but I'm nor familiar with SB varieties, but thank for bringing this papers to my attention, it looks like beautiful and interesting result, definitively something that I want to learn, but I need some time first on SB varieties. | |
| Mar 6, 2013 at 3:36 | comment | added | Benjamin Antieau | A Severi-Brauer variety is a twisted form of projective space over a field. The first example is a smooth projective genus $0$ curve without any points. Such a curve $C$ is the SB variety associated to a quaternion algebra $D$. The derived category of $C$ has a semiorthogonal decomposition $<e_1,e_2>$ where $Hom(e_1,e_1[n])=0$ if $n\neq 0$ and $k$ if $n=0$, while $Hom(e_2,e_2[n])=0$ if $n\neq 0$ and $D$ if $k=0$. Thus, $e_2$ is not an exceptional object in the classical sense, but the object $e_1\oplus e_2$ is a tilting complex. This was worked out in detail by Marcello Bernardara in 2009. | |
| Mar 5, 2013 at 23:18 | comment | added | Jacob Bell | could you expand your comment on Brauer-Severi varieties please? | |
| Mar 5, 2013 at 19:15 | history | answered | Benjamin Antieau | CC BY-SA 3.0 |