Number of full exceptional collections modulo spherical twists for elliptic orbifolds
Algebraic Geometry
2023-11-21 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2311.11110,
title = {Number of full exceptional collections modulo spherical twists for elliptic orbifolds},
author = {Atsushi Takahashi and Hongxia Zhang},
journal= {arXiv preprint arXiv:2311.11110},
year = {2023}
}
Comments
15 pages, 5 tables. arXiv admin note: text overlap with arXiv:2308.04031