Quantum indices and refined enumeration of real plane curves

2015/05/16 by Mikhalkin, Grigory · 2 citations
#14P99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.04338

Abstract

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 π² 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.

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