Vol. 6, No. 2, 2012

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On a conjecture of Kontsevich and Soibelman

Lê Quy Thuong

Vol. 6 (2012), No. 2, 389–404
Abstract

We consider a conjecture of Kontsevich and Soibelman which is regarded as a foundation of their theory of motivic Donaldson–Thomas invariants for noncommutative 3d Calabi–Yau varieties. We will show that, in some certain cases, the answer to this conjecture is positive.

Dedicated to Professor Hà Huy Vui on the occasion of his sixtieth birthday

Keywords
arc spaces, motivic Milnor fiber, motivic zeta function, Newton polyhedron
Mathematical Subject Classification 2010
Primary: 14B05
Secondary: 14B07, 14J17, 32S05, 32S30, 32S55
Milestones
Received: 1 October 2010
Revised: 6 December 2010
Accepted: 19 January 2011
Published: 24 June 2012
Authors
Lê Quy Thuong
École Normale Supérieure
Départment de Mathématiques et Applications
UMR 8553 CNRS
45 rue d’Ulm
75230 Paris cedex 05
France
Institut de Mathématiques de Jussieu
UMR 7586 CNRS
4 place Jussieu
75005 Paris
France