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A note on
Bridgeland stability conditions and Catalan numbers
Jason Lo and Karissa Wong
Vol. 15 (2022), No. 3, 427–432
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Abstract |
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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
Bridgeland stability, Catalan numbers, autoequivalence
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Mathematical Subject Classification
Primary: 14F08, 14J27
Secondary: 05A15, 05E14
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Milestones
Received: 21 April 2021
Revised: 9 October 2021
Accepted: 30 October 2021
Published: 2 December 2022
Communicated by Ravi Vakil
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Authors |
| Jason Lo | |
| Department of Mathematics California State University Northridge, CA United States |
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| Karissa Wong | |
| Department of Mechanical
Engineering University of California Berkeley, CA United States |
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