Bijection between positive clusters and projectively signed exceptional sequences
Abstract
In 2017, Igusa and Todorov gave a bijection between signed exceptional sequences and ordered partial clusters. In this paper, we show that every term in an exceptional sequence is either relatively projective or relatively injective or both and we refine this bijection to one between projectively signed exceptional sequences and ordered partial positive clusters. We also give a characterization of relatively projective/injective objects in terms of supports of the objects in the exceptional sequence.
Cite
@article{arxiv.2312.05997,
title = {Bijection between positive clusters and projectively signed exceptional sequences},
author = {Shujian Chen and Kiyoshi Igusa},
journal= {arXiv preprint arXiv:2312.05997},
year = {2024}
}
Comments
17 pages, v2: the result was already "known" in the finite case, v3: lemmas 1.2, 1.3 are stated in a more useful way, v4: we expanded the paper and changed the title, v5: In Section 4 we calculate the correlation between multiple terms in an exceptional sequence having property rPI (relatively projective and relatively injective)