Exceptional collection of objects on some fake projective planes
Ching-Jui Lai, Sai-Kee Yeung

TL;DR
This paper introduces a new method to establish the existence of exceptional collections on certain fake projective planes, revealing many new examples and contributing to the understanding of their derived categories.
Contribution
The paper presents a novel approach to prove the existence of exceptional collections of length three on fake projective planes with automorphisms, expanding known examples significantly.
Findings
30 fake projective planes support such exceptional collections
Most of these are newly identified examples
The work introduces many new H-phantom categories
Abstract
The purpose of the article is to explain a new method to establish the existence of an exceptional collection of length three for a fake projective plane M with non-trivial automorphism group, related to a conjecture of Galkin-Katzarkov-Mellit-Shinder in 2015. Our method shows that 30 fake projective planes support such a sequence, most of which are new. In particular, this provides many new H-phantom categories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Advanced Algebra and Geometry · Geometric and Algebraic Topology
