Geometry & Topology

Tropical refined curve counting via motivic integration

Johannes Nicaise, Sam Payne, and Franziska Schroeter

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1538186736

Digital Object Identifier
doi:10.2140/gt.2018.22.3175

Mathematical Reviews number (MathSciNet)
MR3858763

Zentralblatt MATH identifier
06945125

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

Keywords
Refined enumerative geometry tropical geometry motivic integration

Citation

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. https://projecteuclid.org/euclid.gt/1538186736


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