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math.RT2026
Syzygy Transformations of Cluster Characters and Geometric Twists
Jiarui Fei
We use the full multiplication formula to study syzygy and suspension of cluster characters. In stably 2-Calabi--Yau Frobenius categories, syzygy and cosyzygy induce inverse automo…
math.RT2025
Hessian Defect, Compatibility Degree, and Canonical Decomposition
Jiarui Fei
We express the difference between dimension and denominator vectors as the rank defect of a Hessian differential. For a very general Jacobi-finite potential, this defect vanishes o…
math.RT2024
On AI's "semistable torsion classes and canonical decompositions"
Jiarui Fei
In this short note, we give two-line proofs for main results in "Semistable torsion classes and canonical decompositions" by Asai-Iyama from a main result in "Tropical -polynomi…