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Log Calabi–Yau surfaces and Jeffrey–Kirwan residues

Part of: Surfaces and higher-dimensional varieties Representation theory of rings and algebras General mathematical topics and methods in quantum theory

Published online by Cambridge University Press:  04 March 2024

RICCARDO ONTANI  and
JACOPO STOPPA
RICCARDO ONTANI
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy. e-mails:rontani@sissa.it, jstoppa@sissa.it
JACOPO STOPPA
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy. e-mails:rontani@sissa.it, jstoppa@sissa.it
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Abstract

We prove an equality, predicted in the physical literature, between the Jeffrey–Kirwan residues of certain explicit meromorphic forms attached to a quiver without loops or oriented cycles and its Donaldson–Thomas type invariants.

In the special case of complete bipartite quivers we also show independently, using scattering diagrams and theta functions, that the same Jeffrey–Kirwan residues are determined by the the Gross–Hacking–Keel mirror family to a log Calabi–Yau surface.

MSC classification

Primary: 14J33: Mirror symmetry 16G20: Representations of quivers and partially ordered sets
Secondary: 81Q60: Supersymmetry and quantum mechanics
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 3 , May 2024 , pp. 547 - 592
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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