Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF FULL EXCEPTIONAL COLLECTIONS OF LINE BUNDLES ON THREE BLOW-UPS OF ℙ3

  • Liu, Wanmin (Center for Geometry and Physics Institute for Basic Science (IBS)) ;
  • Yang, Song (Center for Applied Mathematics Tianjin University) ;
  • Yu, Xun (Center for Applied Mathematics Tianjin University)
  • Received : 2018.03.27
  • Accepted : 2018.10.12
  • Published : 2019.03.01
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Abstract

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.

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References

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