A note on Bridgeland stability conditions and Catalan numbers
Algebraic Geometry
2022-12-21 v3 Mathematical Physics
Combinatorics
math.MP
Abstract
In this short note, we describe a problem in algebraic geometry where the solution involves Catalan numbers. More specifically, we consider the derived category of coherent sheaves on an elliptic surface, and the action of its autoequivalence group on its Bridgeland stability manifold. In solving an equation involving this group action, the generating function of Catalan numbers arises, allowing us to use asymptotic estimates of Catalan numbers to arrive at a bound for the solution set.
Keywords
Cite
@article{arxiv.2012.12851,
title = {A note on Bridgeland stability conditions and Catalan numbers},
author = {Jason Lo and Karissa Wong},
journal= {arXiv preprint arXiv:2012.12851},
year = {2022}
}
Comments
5 pages. The introduction has been expanded at the referee's suggestion. Other minor edits