Motivic Donaldson–Thomas invariants for the one-loop quiver with potential

Davison, Ben¹ ; Meinhardt, Sven²

¹ Section de mathématiques, École Polytechnique Fédérale de Lausanne, Station 8, Bâtiment MA, CH-1015 Lausanne, Switzerland
² Fachbereich C — Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaussstrasse 20, D-42119 Wuppertal, Germany

Geometry & topology, Tome 19 (2015) no. 5, pp. 2535-2555.

Résumé

We compute the motivic Donaldson–Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson–Thomas invariants to use in an essential way the full machinery of $\widehat{\mu }$–equivariant motives, for which we prove a dimensional reduction result similar to that of Behrend, Bryan and Szendrői in their study of degree-zero motivic Donaldson–Thomas invariants. Our result differs from theirs in that it involves nontrivial monodromy.

Détail

DOI : 10.2140/gt.2015.19.2535

Classification : 14N35, 14D23
Keywords: motivic Donaldson–Thomas theory, vanishing cycles, quivers

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