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Preprint Number 1196

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1196. Johannes Nicaise and Sam Payne
A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory

Submission date: 29 March 2017


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 semi-algebraic 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.

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Full text arXiv 1703.10228: pdf, ps.

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