Quantum indices of real plane curves and refined enumerative geometry

Saturday, 16 May, 2015

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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 π^2 times the quantum index of the curve. We use the quantum index to refine real enumerative geometry in a way consistent with the Block-Göttsche invariants from tropical enumerative geometry.


Grigory Mikhalkin