We introduce a quantum index for oriented real curves inside toric varieties. This quantum index is related to the computation of the area of the amoeba of the curve for some chosen 2 2 -form. We then make a refined signed count of oriented real rational curves solution to some enumerative problem. This generalizes the 2017 results of Mikhalkin to higher dimension. Finally, we use the tropical approach to relate these new refined invariants to previously known tropical refined invariants.
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Thomas Blomme (2023) studied this question.
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