Abstract
AbstractWe construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
Publisher
Springer Science and Business Media LLC
Reference13 articles.
1. Böhning, C., Graf von Bothmer, H.-C., Katzarkov, L., Sosna, P.: Determinantal Barlow surfaces and phantom categories. J. Eur. Math. Soc. 17(7), 1569–1592 (2015)
2. Chang, W., Haiden, F., Schroll, S.: Braid group actions on branched coverings and full exceptional sequences (2023). arXiv:2301.04398v2 [math.RT]
3. Ciliberto, C., Miranda, R.: Homogeneous interpolation on ten points. J. Algebraic Geom. 20(4), 685–726 (2011)
4. Dumnicki, M., Jarnicki, W.: New effective bounds on the dimension of a linear system in $\mathbb{P}^{2}$. J. Symb. Comput. 42(6), 621–635 (2007)
5. Efimov, A.: Private communication. Bielefeld (2023)
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