Geometry & Topology

Tropical refined curve counting via motivic integration

Johannes Nicaise, Sam Payne, and Franziska Schroeter

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We propose a geometric interpretation of Block and Göttsche’s refined tropical curve counting invariants in terms of virtual χ 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 χ y –genus to Euler characteristic.

Article information

Geom. Topol., Volume 22, Number 6 (2018), 3175-3234.

Received: 7 April 2016
Revised: 6 February 2018
Accepted: 27 March 2018
First available in Project Euclid: 29 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E18: Arcs and motivic integration 14G22: Rigid analytic geometry 14T05: Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]

Refined enumerative geometry tropical geometry motivic integration


Nicaise, Johannes; Payne, Sam; Schroeter, Franziska. Tropical refined curve counting via motivic integration. Geom. Topol. 22 (2018), no. 6, 3175--3234. doi:10.2140/gt.2018.22.3175.

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