Quantum indices and refined enumeration of real plane curves

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.

Full Text (PDF format)

Received 4 January 2016

Received revised 22 November 2017

Accepted 6 December 2017

Published 31 January 2018