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The
$3$-fold K-theoretic DT/PT vertex correspondence holds
Nikolas Kuhn, Henry Liu and Felix Thimm |
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Geometry & Topology 30 (2026) 71–154
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DOI: 10.2140/gt.2026.30.71
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Abstract |
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We prove the -fold DT/PT correspondence for K-theoretic vertices via wall-crossing techniques. We provide two different setups, following Mochizuki and following Joyce; both reduce the problem to -combinatorial identities on word rearrangements. An important technical step is the construction of symmetric almost-perfect obstruction theories (APOTs) on auxiliary moduli stacks, e.g., master spaces, from the symmetric DT or PT obstruction theory. For this, we introduce symmetrized pullbacks of symmetric obstruction theories along smooth morphisms to Artin stacks. |
Keywords
Donaldson–Thomas theory, Pandharipande–Thomas stable pairs,
K-theory, equivariant vertex, DT/PT correspondence,
wall-crossing
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Mathematical Subject Classification
Primary: 14N35
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References |
Publication
Received: 4 March 2024
Revised: 17 April 2025
Accepted: 16 May 2025
Published: 19 January 2026
Proposed: Mark Gross
Seconded: Jim Bryan, Dan Abramovich
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Authors |
| Nikolas Kuhn | |
| Department of Mathematics University of Oslo Oslo Norway |
Mathematical Institute University of Oxford Oxford United Kingdom |
| Henry Liu | |
| Kavli IPMU Tokyo Japan |
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| Felix Thimm | |
| Department of Mathematics University of Oslo Oslo Norway |
Department of Mathematics University of British Columbia Vancouver, BC Canada |
| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
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