A Computer Algebra Approach to sheaves over Weighted Projective Lines

Abstract

The theoretical background of the TUBULAR package, developed for a computer algebra treatment of sheaves over weighted projective (tubular) lines is presented. The package is also of interest for classifying indecomposable modules over finite dimensional tubular algbras, resp. G-equivariant sheaves over elliptic curves with respect to certain actions of finite groups. The encoding of indecomposable sheaves by a set of discrete data (using the tubular structure of coh X) and the effective method of determining the class [$\mathcal{F}$] of indecomposable $\mathcal{F} \in coh \mathbb{X}$ in the Grothendieck group ${{K}_{0}}\mathbb{X}$ (based on the telescoping functor technique) are explained. Certain additional facts improving efficiency of this method are discussed.