Tilting objects in the stable category of vector bundles on the weighted projective line of type (2,2,2,2;\lambda)

TL;DR

This paper constructs a specific tilting object in the stable category of vector bundles on a weighted projective line of type (2,2,2,2;), revealing its endomorphism algebra as a canonical algebra.

Contribution

It introduces a new tilting object in the stable category of vector bundles on a weighted projective line of this specific type.

Findings

The tilting object consists of five rank two bundles and one rank three bundle.

The endomorphism algebra of this tilting object is a canonical algebra of the same type.

This construction advances understanding of the category's structure.

Abstract

We construct a tilting object for the stable category of vector bundles on a weighted projective line X of type (2,2,2,2;\lambda), consisting of five rank two bundles and one rank three bundle, whose endomorphism algebra is a canonical algebra associated with X of type (2,2,2,2).