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Can anybody give me the reference where this counter-example is explained in detail?. Consists on the following Bondal considered a quiver $Q$ with some relations and proved that $D(Q)$ has two different semi-orthogonal decompositions, of length 3 and 2. Also, I don't know anything about quivers, do you think that there is a way to understand this result without a lot of background? Thanks!

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http://arxiv.org/abs/1304.0903

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  • $\begingroup$ I already knew that papper, the thing is that there it explains what Bondal proved, but doesn't give a detailed proof nor a reference $\endgroup$
    – Miguel
    Commented May 17, 2013 at 16:48
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    $\begingroup$ The reason for nonextendability is the fact that the Euler form $\chi(-,-)$ on the orthogonal subcategory $P^\perp$ is skew-symmetric, and so $P^\perp$ does not have exceptional objects. $\endgroup$
    – Sasha
    Commented May 17, 2013 at 19:28

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