Modules attached to extension bundles

TL;DR

This paper investigates modules over wild canonical algebras linked to extension bundles on weighted projective lines, providing matrix-based construction methods and extending concepts to general weight types.

Contribution

It introduces a matrix-based approach to construct modules attached to extension bundles and generalizes the concept to arbitrary weight types.

Findings

Modules can be constructed using matrices related to algebra relations

Extension bundle concepts are extended to general weight types

A method to compute matrices via cokernels of line bundle maps

Abstract

In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients related to the relations of the considered algebra. Moreover, we expand the concept of extension bundles over weighted projective lines with three weights to general weight type and establish similar results in this situation. Finally, we present a method to compute matrices for all modules attached to extension bundles using cokernels of maps between direct sums of line bundles.