On tubular tilting objects in the stable category of vector bundles

TL;DR

This paper investigates the stable category of vector bundles on weighted projective lines of weight three, constructing specific tilting objects with tubular endomorphism algebras for genus one cases using cluster tilting theory.

Contribution

It introduces new tilting objects with tubular endomorphism algebras in the stable category of vector bundles on weighted projective lines of weight three, employing cluster tilting techniques.

Findings

Identified important triangles in the stable category.

Constructed tilting objects with tubular endomorphism algebras.

Applied cluster tilting theory to genus one cases.

Abstract

The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular endomorphism algebras for the case of genus one via cluster tilting theory.