2024/09/19 by Abel Castorena, Castorena, Abel, George H. Hitching +1
Engineering · Physics and Astronomy · #14D20 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum chaos and dynamical systems #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2409.12794
openalex publication_date 2024/09/19 · openalex created_date 2024/10/25 · openalex updated_date 2026/07/28
There is a well studied notion of GIT-stability for coherent systems over curves, which depends on a real parameter α. For generated coherent systems, there is a further notion of stability derived from Mumford's definition of linear stability for varieties in projective space. Let αS be close to zero and αL ≫ 0. We show that a generated coherent system which is αS-stable and linearly stable is αL-stable, and give examples showing that without further assumptions, there are no other implications between these three types of stability. We observe that several of the systems constructed have stable dual span bundle, including systems which are not α-semistable for any value of α. We use this to prove a case of Butler's conjecture for systems of type (2, d, 5).