Vol. 11, No. 6, 2017

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
The motivic Donaldson–Thomas invariants of ($-$2)-curves

Ben Davison and Sven Meinhardt

Vol. 11 (2017), No. 6, 1243–1286
Abstract

We calculate the motivic Donaldson–Thomas invariants for (2)-curves arising from 3-fold flopping contractions in the minimal model program. We translate this geometric situation into the machinery developed by Kontsevich and Soibelman, and using the results and framework developed earlier by the authors we describe the monodromy on these invariants. In particular, in contrast to all existing known Donaldson–Thomas invariants for small resolutions of Gorenstein singularities these monodromy actions are nontrivial.

Keywords
Donaldson–Thomas theory, minus two curves, motivic invariants
Mathematical Subject Classification 2010
Primary: 14N35
Milestones
Received: 6 February 2016
Revised: 23 November 2016
Accepted: 1 February 2017
Published: 16 August 2017
Authors
Ben Davison
School of Mathematics and Statistics
University of Glasgow
15 University Gardens
Glasgow
G128QW
United Kingdom
Sven Meinhardt
School of Mathematics and Statistics
University of Sheffield
Hicks Building, Hounsfield Road
Sheffield
S37RH
United Kingdom