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Block–Göttsche invariants from wall-crossing

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

Published online by Cambridge University Press:  12 March 2015

S. A. Filippini  and
J. Stoppa
S. A. Filippini
Affiliation:
Institut für Mathematik, Universität Zürich, Wintherthurerstrasse 190, 8057 Zürich, Schweiz email saraangela.filippini@math.uzh.ch
J. Stoppa
Affiliation:
Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, via Ferrata 1, 27100 Pavia, Italia email jacopo.stoppa@unipv.it
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Abstract

We show how some of the refined tropical counts of Block and Göttsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative $q$-deformed Gromov–Witten invariants. We prove that this coincides with another natural $q$-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined.

Keywords

tropical countswall-crossingGromov–Witten invariants

MSC classification

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
Secondary: 14T05: Tropical geometry 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 8 , August 2015 , pp. 1543 - 1567
Copyright
© The Authors 2015 

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