Hall Polynomials for Weighted projective lines

2025/02/23 by Jiayi Chen, Chen, Jiayi, Bangming Deng +3
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2502.16543

Abstract

This paper deals with the triangle singularity defined by the \linebreak equation f=X₁^p₁+X₂^p₂+X₃^p₃ for weight triple (p₁,p₂,p₃), as well as the category of coherent sheaves over the weighted projective line \mathbbX defined by f. We calculate Hall polynomials associated to extensions bundles, line bundles and torsion sheaves over \mathbbX. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi [J. Pure Appl. Alg. \bf 228 (2024)].

Related

• Hall polynomials for tame type
• Lectures on Hall algebras
• CoHAs of Torsion Sheaves on Weighted Projective Curves
• Hall polynomials for affine quivers
• Weighted projective lines as fine moduli spaces of quiver representations