Quantum indices and refined enumeration of real plane curves
Grigory Mikhalkin · Acta Mathematica · 2017
We associate a half-integer number, called {\em 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 $π^2$ times the quantum index of the curve and thus has a discrete spectrum of values. We use the quantum index to refine real enumerative geometry in a way consistent with the Block-Göttsche invariants from tropical enumerative geometry.