English

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