Abstract
We associate a half-integer number, called the quantum index, to algebraic curves in the real plane satisfying to certain conditions. The area encompassed by the logarithmic image of such curves is equal to $\pi^2$ times the quantum index of the curve, and thus has a discrete spectrum of values. We use the quantum index to refine enumeration of real rational curves in a way consistent with the Block–Göttsche invariants from tropical enumerative geometry.
Citation
Grigory Mikhalkin. "Quantum indices and refined enumeration of real plane curves." Acta Math. 219 (1) 135 - 180, September 2017. https://doi.org/10.4310/ACTA.2017.v219.n1.a5