Year: 2026
Type: preprint
Abstract: The TF-cone conjecture of Asai and Iyama predicts that the TF equivalence class of an integral $g$-vector is the open cone generated by the canonical summands of all its positive multiples. We give a counterexample to this conjecture. For the tensor product of the three-arrow Kronecker algebra with the path algebra of $s\to t$, a vector $w$ has a two-dimensional TF equivalence class, whereas every positive integral multiple $mw$ is generically indecomposable. The cone generated by these canonical summands is therefore a single ray. The same example disproves the relative-interior version proposed by Haerizadeh and Yassemi.
Source: arXiv (Cornell University)
Authors: Yan, Jindong, Zhu, Shenglin
Institution: Fudan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221772514