The existence of a maximal green sequence is not invariant under quiver mutation

Greg Muller

The existence of a maximal green sequence is not invariant under quiver mutation

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arxiv 1503.04675 v4 pith:NZKJ3VU5 submitted 2015-03-16 math.QA math.CO

Greg Muller This is my paper · ORCID

classification math.QAmath.CO

keywords greenmaximalsequencequiveradmitdeterminesdiagramsexistence

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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.

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