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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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참고문헌 (36)
참고문헌 신청
V. Alexeev / 2013 / Derived categories of Burniat surfaces and exceptional collections / Math. Ann 357(2):743~759
A. Auel / 2017 / Cycles, derived categories, and rationality, in Surveys on recent developments in algebraic geometry / Surveys on recent developments in algebraic geometry, Proc. Sympos. Pure Math. 95:199~266
A. A. Beılinson / 1978 / Coherent sheaves on Pn and problems in linear algebra / Funktsional. Anal. i Prilozhen 12(3):68~69
Ch. B¨ohning / 2015 / Determinantal Barlow surfaces and phantom categories / J. Eur. Math. Soc. (JEMS) 17(5):1569~1592
C. Bohning / 2013 / On the derived category of the classical Godeaux surface / Adv. Math 243:203~231
A. Auel / 2017 / Cycles, derived categories, and rationality, in Surveys on recent developments in algebraic geometry / Surveys on recent developments in algebraic geometry, Proc. Sympos. Pure Math. 95:199~266
A. A. Beılinson / 1978 / Coherent sheaves on Pn and problems in linear algebra / Funktsional. Anal. i Prilozhen 12(3):68~69
Ch. B¨ohning / 2015 / Determinantal Barlow surfaces and phantom categories / J. Eur. Math. Soc. (JEMS) 17(5):1569~1592
C. Bohning / 2013 / On the derived category of the classical Godeaux surface / Adv. Math 243:203~231
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