Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 10 (2019), 1843-1886.
A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory
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.
Duke Math. J., Volume 168, Number 10 (2019), 1843-1886.
Received: 5 September 2017
Revised: 19 November 2018
First available in Project Euclid: 7 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14E18: Arcs and motivic integration 14T05: Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
Nicaise, Johannes; Payne, Sam. A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory. Duke Math. J. 168 (2019), no. 10, 1843--1886. doi:10.1215/00127094-2019-0003. https://projecteuclid.org/euclid.dmj/1559894420