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
P3 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.Comment: 28 pages. To appear in Journal of the Korean Mathematical Society, A
previous version with a different title appeared as [CGP17025] at
https://cgp.ibs.re.kr/archive/preprints/201