A Phantom on a Rational Surface
arXiv:2304.01269 · doi:10.1007/s00222-023-01234-0
Abstract
We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 points in general position. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
arXiv comment6 pages, added application to presilting objects in introduction
References in corpus (5)
- Geometric Phantom Categories
- Determinantal Barlow surfaces and phantom categories
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
- Exceptional collections, and the Neron-Severi lattice for surfaces
- Finite-dimensional differential graded algebras and their geometric realizations