The t-stabilities and t-structures for the Weighted Projective Line of Type (2,1)

Abstract

We study the t-stabilities on the bounded derived category $D^{b}(\text {coh }\mathbb {X})$ of coherent sheaves on the weighted projective line $\mathbb {X}$ of type (2,1). A complete classification of both t-stabilities and bounded t-structures on $D^{b}(\text {coh }\mathbb {X})$ is given.