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arXiv · 1703.10228

A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory

Johannes Nicaise·Sam Payne
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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 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 L\^e Quy Thuong. Both of these conjectures emerged in the context of motivic Donaldson-Thomas theory.

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Johannes Nicaise, Sam Payne. 2017-03-29. A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory. https://doi.org/10.1215/00127094-2019-0003

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