The braid group action on exceptional sequences for weighted projective lines

2021/02/09 by Edson Ribeiro Alvares, Alvares, Edson R., Eduardo N. Marcos +3
Mathematics · #15H05 #16G20 #16G99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2102.04584

openalex publication_date 2021/02/09 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We give a new and intrinsic proof of the transitivity of the braid group action on the set of full exceptional sequences of coherent sheaves on a weighted projective line. We do not use here the corresponding result of Crawley-Boevey for modules over hereditary algebras. As an application we prove that the strongest global dimension of the category of coherent sheaves on a weighted projective line \XX does not depend on the parameters of \XX. Finally we prove that the determinant of the matrix obtained by taking the values of n \ZZ-linear functions defined on the Grothendieck group K₀(\XX) ≃ \ZZⁿ of the elements of a full exceptional sequence is an invariant, up to sign.

Related

• Combinatorial Approaches to Exceptional Sequences for Weighted Projective Lines of Type (p,q)
• Braid group actions on branched coverings and full exceptional sequences
• Braid group actions on derived categories of coherent sheaves
• A remark on braid group actions on coherent sheaves
• A simple algebraic proof of the non-transitivity of the braid group action on full exceptional sequences