5 papers
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…
Cluster Geometry of Universal Schubert Polynomials I: Geometric Bases and Schubert Transitions
Jiarui Fei
We study Fulton's universal Schubert polynomials as regular functions on the upper unitriangular group . The standard triangular cluster structure associate…
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…
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…
General Presentations of Algebras and Foundations of -tilting Theory
Harm Derksen, Jiarui Fei
In this short note, we explain how the main results in "-tilting theory" by Adachi-Iyama-Reiten follow from the results in Section 5 of "General presentations of algebras" by De…