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arXiv · 2107.07286

Refined count of real oriented rational curves

Thomas Blomme
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Abstract

We introduce a \textit{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-form. We then make a refined signed count of oriented real rational curves solution to some enumerative problem. This generalizes the results from G. Mikhalkin arXiv:1505.04338 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. 2021-07-15. Refined count of real oriented rational curves. https://arxiv.org/abs/2107.07286

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