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15 July 2019 A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory
Johannes Nicaise, Sam Payne
Duke Math. J. 168(10): 1843-1886 (15 July 2019). DOI: 10.1215/00127094-2019-0003

Abstract

We present a new tool for the calculation of Denef and Loeser’s motivic nearby fiber and motivic Milnor fiber: a motivic Fubini theorem for the tropicalization map, based on Hrushovski and Kazhdan’s theory of motivic volumes of semialgebraic sets. As applications, we prove a conjecture of Davison and Meinhardt on motivic nearby fibers of weighted homogeneous polynomials, and give a very short and conceptual new proof of the integral identity conjecture of Kontsevich and Soibelman, first proved by Lê Quy Thuong. Both of these conjectures emerged in the context of motivic Donaldson–Thomas theory.

Citation

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Johannes Nicaise. Sam Payne. "A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory." Duke Math. J. 168 (10) 1843 - 1886, 15 July 2019. https://doi.org/10.1215/00127094-2019-0003

Information

Received: 5 September 2017; Revised: 19 November 2018; Published: 15 July 2019
First available in Project Euclid: 7 June 2019

zbMATH: 07108021
MathSciNet: MR3983293
Digital Object Identifier: 10.1215/00127094-2019-0003

Subjects:
Primary: 14N35
Secondary: 14E18, 14T05

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 10 • 15 July 2019
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