A chamber decomposition of tangency conditions for log stable maps to toric surfaces makes the Grothendieck class of the moduli space constant within chambers defined by fixed cyclic orderings.
[CJM10] Renzo Cavalieri, Paul Johnson, and Hannah Markwig.Chamber Structure of Double Hurwitz numbers
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Cut and paste invariants of moduli spaces of stable maps to toric surfaces
A chamber decomposition of tangency conditions for log stable maps to toric surfaces makes the Grothendieck class of the moduli space constant within chambers defined by fixed cyclic orderings.