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Motivic Donaldson–Thomas invariants and the Kac conjecture

Part of: Representation theory of rings and algebras Projective and enumerative geometry

Published online by Cambridge University Press:  28 February 2013

Sergey Mozgovoy
Sergey Mozgovoy*
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK email [email protected]
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Abstract

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We derive some combinatorial consequences from the positivity of Donaldson–Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for quivers having at least one loop at every vertex.

Keywords

Donaldson–Thomas invariantsKac conjecture

MSC classification

Secondary: 16G20: Representations of quivers and partially ordered sets 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 3 , March 2013 , pp. 495 - 504
Copyright
© The Author(s) 2013 

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