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

TL;DR

This paper characterizes bounded t-structures on the derived category of coherent sheaves over weighted projective lines with virtual genus ≤ 1, linking their classification to that of finite-dimensional hereditary algebras.

Contribution

It provides a description of bounded t-structures on these derived categories using recollement and HRS-tilt, reducing the classification problem to finite-dimensional hereditary algebras.

Findings

Bounded t-structures are described via recollement and HRS-tilt.

Classification reduces to that of finite-dimensional hereditary algebras.

The approach applies to weighted projective lines with virtual genus ≤ 1.

Abstract

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 $\leq 1$. 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.