On a conjecture of Kontsevich and Soibelman

Quy Thuong, Lê

doi:10.2140/ant.2012.6.389

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On a conjecture of Kontsevich and Soibelman

Lê Quy Thuong

Vol. 6 (2012), No. 2, 389–404

DOI: 10.2140/ant.2012.6.389

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 $3 d$ 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

Vol. 6, No. 2, 2012