arXiv subjects

Mingfa Chen

Publications and source records attributed to Mingfa Chen.

3 recordsLinked to original sources

arXiv2025

Semi-orthogonal decompositions via t-stabilities

In this paper we introduce a local-refinement procedure to investigate finite t-stabilities on a triangulated category, and show a direct sufficient condition for a finite t-stability to be finite finest. We classify all finite finest t-stabilities for certain triangulated categories, including those from the projective plane, weighted projective lines, and finite acyclic quivers. As applications, we obtain a simple classification of semi-orthogonal decompositions (SOD) for these categories. Furthermore, we study the connectedness of SODs by a reduction method and give an easily verified criterion for it.

math.CT↗

arXiv2023

Exchange graphs and Ext-quivers of hearts of tube categories

In this paper we introduce the notion of pre-simple-minded collection (pre-SMC) of type $\mathbb{A}$ in the bounded derived categories $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$ of tube categories $\textbf{T}_{p}$ of rank $p$. This provides an effective approach to classify the hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$. We then use this classification to prove the exchange graph of hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$ is connnected. Further, we classify the Ext-quivers of hearts in $\mathcal{D}^{b} (${\rm{\textbf{T}}}$_p)$. As an application, we show that the space of Bridgeland stability conditions on $\mathcal{D}^{b}(${\rm{\textbf{T}}}$_p)$ is connected.

math.RA↗

arXiv2023

Stability approach to torsion pairs on abelian categories

In this paper we introduce a local-refinement procedure to investigate stability data on an abelian category, and provide a sufficient and necessary condition for a stability data to be finest. We classify all the finest stability data for the categories of coherent sheaves over certain weighted projective curves, including the classical projective line, smooth elliptic curves and certain weighted projective lines. As applications, we obtain a classification of torsion pairs for these categories via stability data approach. As a by-product, a new proof for the classification of torsion pairs in any tube category is also provided.

math.RT↗