ACM tilting bundles on a Geigle-Lenzing projective plane of type (2,2,2,p)

2025/06/16 by Jianmin Chen, Chen, Jianmin, Shiquan Ruan +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.13376

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

Let \mathbbX be a Geigle-Lenzing projective plane of type (2,2,2,p) and coh \mathbbX the category of coherent sheaves on \mathbbX. This paper is devoted to study ACM tilting bundles over \mathbbX, that is, tilting objects in the derived category D^{\rm b}(coh \mathbbX) that are also ACM bundles. We show that a tilting bundle consisting of line bundles is the 2-canonical tilting bundle up to degree shift. We also provide a program to construct ACM tilting bundles, which give a rich source of (almost) 2-representation infinite algebras. As an application, we give a classification result of ACM tilting bundles.

Citations

• Brieskorn-Pham singularities via ACM bundles on Geigle-Lenzing projective spaces
• The 3-Preprojective Algebras Of Type Ã
• Geometric model for weighted projective lines of type (p,q)
• On 2-representation infinite algebras arising from dimer models
• Higher representation infinite algebras from McKay quivers of metacyclic groups
• A recollement approach to Geigle-Lenzing weighted projective varieties
• Higher APR tilting preserves n-representation infiniteness
• Representation theory of Geigle-Lenzing complete intersections
• Tilting bundles on orders on P^d
• Tilting bundles and the "missing part" on the weighted projective line of type (2, 2, n)
• Triangle singularities, ADE-chains, and weighted projective lines
• Stable categories of Cohen-Macaulay modules and cluster categories
• Tilting and cluster tilting for quotient singularities
• Homological mirror symmetry for Brieskorn-Pham singularities
• ACM bundles on cubic surfaces
• Grothendieck groups and tilting objects

Related

• Tilting bundles and the "missing part" on the weighted projective line of type (2, 2, n)
• A recollement approach to Geigle-Lenzing weighted projective varieties
• An open question for d-tilting bundles on Geigle-Lenzing projective spaces
• Canonical tilting bundles: the first nonabelian examples
• Tilting bundles on orders on P^d