A new phantom on a rational surface
Algebraic Geometry
2025-11-11 v1
Abstract
We construct a universal phantom subcategory on the blow-up of the complex projective plane in 11 general points. This phantom subcategory is the orthogonal complement of a non-full exceptional collection of line bundles of maximal length. It provides a new counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov. The first counterexample was constructed by Krah [Invent. Math. {\bf 235} (2024),1009--1018]. As an application, we construct a new co-connective DG-algebra whose derived category is a phantom.
Keywords
Cite
@article{arxiv.2511.07114,
title = {A new phantom on a rational surface},
author = {Shihao Ma and Yirui Xiong and Song Yang},
journal= {arXiv preprint arXiv:2511.07114},
year = {2025}
}
Comments
10 pages. Comments are very welcome