Bounded t-structures on the bounded derived category of coherent sheaves over a weighted projective line

We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category ${\mathcal{D}}^b(\mathbb{X})$ of coherent sheaves over a weighted projective line $\mathbb{X}$ of virtual genus $\le 1$. We will see from our description that the combinatorics in classification of bounded t-structures on ${\mathcal{D}}^b(\mathbb{X})$ can be reduced to that in classification of bounded t-structures on bounded derived categories of finite dimensional right modules over representation-finite finite dimensional hereditary algebras.