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Aug 31, 2018 at 22:41 comment added Ennio Mori cone Bondal and Polishchuk's "Homological properties of associative algebras: the method of helices." shows that a variety with a full exceptional collection of length $\dim X+1$ must be a fano variety.
Aug 31, 2018 at 16:18 vote accept CommunityBot
Aug 31, 2018 at 16:04 history edited Sasha
I added the "open-problems" tag.
Aug 31, 2018 at 15:45 answer added Sasha timeline score: 8
Aug 31, 2018 at 14:39 comment added Leo Alonso Unfortunately, I'm not aware of such a reference. In fact I can't figure out any example. On the other hand, you have a full description of the derived category of Abelian varieties, though not through an exceptional collection (if I'm not mistaken).
Aug 31, 2018 at 14:36 comment added user74900 @LeoAlonso is it? I did not know it. If you could post a link to a paper where it is stated to be an open problem, I would accept it as an answer.
Aug 31, 2018 at 14:28 comment added Leo Alonso Perhaps this question should count as an "open problem".
Aug 31, 2018 at 9:23 history edited user74900 CC BY-SA 4.0
added 13 characters in body
Aug 31, 2018 at 8:10 history asked user74900 CC BY-SA 4.0