Wide subcategories of a domestic weighted projective line

2023/06/18 by Yiyu Cheng, Cheng, Yiyu
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.10566

openalex publication_date 2023/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a weighted projective line X, a wide subcategory of the category coh-X of coherent sheaves over X is called c-invariant if it is closed under the grading shift of the canonical element c. We proved that a c-invariant wide subcategory of coh-X containing a vector bundle is the perpendicular category of a torsion exceptional sequence. If X is of dometic type, then the poset of wide subcategories of coh-X is the union of the poset of wide subcategories generated by an exceptional sequence and the poset of c-invariant wide subcategories.

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