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http://dx.doi.org/10.4134/JKMS.j180204

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)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 387-419 More about this Journal
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.
Keywords
derived category of coherent sheaves; full exceptional collection; semiorthogonal decomposition;
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