Invited by Prof. Yanfeng Luo and Dr.Bing Duan, Prof. Changjian Fu and Associate Prof. Shengfei Geng from Sicuan University will give lectures online.

Title:On cluster categories of weighted projective lines with at most three weights

Time: 9:00 a.m.,Mar. 18th, 2021

Conference ID:95775830584( Tencent Conference) , PW:125914

Web Site:：https://meeting.tencent.com/s/coCmTiarQPPu

Abstract:

Let $\mathbb{X}$ be a weighted projective line and $\mathcal{C}_\mathbb{X}$ the associated cluster category. It is known that $\mathcal{C}_\mathbb{X}$ can be realized as a generalized cluster category of quiver with potential. In this talk, under the assumption that $\mathbb{X}$ has at most three weights or is of tubular type, we prove that if the generalized cluster category $\mathcal{C}_{(Q,W)}$ of a Jacobi-finite non-degenerate quiver with potential $(Q,W)$ shares a 2-CY tilted algebra with $\mathcal{C}_\mathbb{X}$, then $\mathcal{C}_{(Q,W)}$ is triangle equivalent to $\mathcal{C}_\mathbb{X}$. As a byproduct, a 2-CY tilted algebra of $\mathcal{C}_\mathbb{X}$ is determined by its quiver provided that $\mathbb{X}$ has at most three weights. In the end, for any weighted projective line $\mathbb{X}$ with at most three weights, we also obtain a realization of $\mathcal{C}_\mathbb{X}$ via Buan-Iyama-Reiten-

Scott's construction of $2$-CY categories arising from preprojective algebras. This talk is based on joint work with Changjian Fu.