Number of full exceptional collections modulo spherical twists for elliptic orbifolds

• DOI: 10.1016/j.jalgebra.2024.12.021
• Publication Date: 2025-01-08T23:51:15Z
• Authors: Atsushi Takahashi; Hongxia Zhang
• Keywords: Mathematics - Algebraic Geometry; FOS: Mathematics; Algebraic Geometry (math.AG)

This paper calculates the number of full exceptional collections modulo an action of a group as the set generated by spherical twists for an abelian category of coherent sheaves on an orbifold projective line with a zero orbifold Euler characteristic. This is done by a recursive formula naturally generalizing the one for the Dynkin case by Deligne whose categorical interpretation is due to Obaid-Nauman-Shammakh-Fakieh-Ringel and an abelian category of coherent sheaves on an orbifold projective line with a positive orbifold Euler characteristic is due to Otani-Shiraishi-Takahashi.<br/>15 pages, 5 tables. arXiv admin note: text overlap with arXiv:2308.04031<br/>