• Title/Summary/Keyword: semiorthogonal decomposition

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CLASSIFICATION OF FULL EXCEPTIONAL COLLECTIONS OF LINE BUNDLES ON THREE BLOW-UPS OF ℙ3

  • Liu, Wanmin;Yang, Song;Yu, Xun
    • Journal of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.387-419
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    • 2019
  • A fullness conjecture of Kuznetsov says that if a smooth projective variety X admits a full exceptional collection of line bundles of length l, then any exceptional collection of line bundles of length l is full. In this paper, we show that this conjecture holds for X as the blow-up of ${\mathbb{P}}^3$ at a point, a line, or a twisted cubic curve, i.e., any exceptional collection of line bundles of length 6 on X is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such X.