The existence of a maximal green sequence is not invariant under quiver mutation
Quantum Algebra
2016-06-28 v4 Combinatorics
Abstract
This note provides a quiver which does not admit a maximal green sequence, but which is mutation-equivalent to a quiver which does admit a maximal green sequence. The proof uses the `scattering diagrams' of Gross-Hacking-Keel-Kontsevich to show that a maximal green sequence for a quiver determines a maximal green sequence for any induced subquiver.
Keywords
Cite
@article{arxiv.1503.04675,
title = {The existence of a maximal green sequence is not invariant under quiver mutation},
author = {Greg Muller},
journal= {arXiv preprint arXiv:1503.04675},
year = {2016}
}
Comments
19 pages, 18 figures, comments encouraged, fixed incorrect formula for mutation of scattering diagram