#### Volume 22, issue 6 (2018)

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Tropical refined curve counting via motivic integration

### Johannes Nicaise, Sam Payne and Franziska Schroeter

Geometry & Topology 22 (2018) 3175–3234
##### Abstract

We propose a geometric interpretation of Block and Göttsche’s refined tropical curve counting invariants in terms of virtual ${\chi }_{-y}$ specializations of motivic measures of semialgebraic sets in relative Hilbert schemes. We prove that this interpretation is correct for linear series of genus 1, and in arbitrary genus after specializing from ${\chi }_{-y}$–genus to Euler characteristic.

##### Keywords
Refined enumerative geometry, tropical geometry, motivic integration
##### Mathematical Subject Classification 2010
Primary: 14E18, 14G22, 14T05