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We introduce a \textit{quantum index} for oriented real curves inside toricvarieties. This quantum index is related to the computation of the area of theamoeba of the curve for some chosen 2-form. We then make a refined signed countof oriented real rational curves solution to some enumerative problem. Thisgeneralizes the results from G. Mikhalkin arXiv:1505.04338 to higher dimension.Finally, we use the tropical approach to relate these new refined invariants topreviously known tropical refined invariants.

Refined count of real oriented rational curves