The 3-fold K-theoretic DT/PT vertex correspondence holds
Abstract
We prove the 3-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 q-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 of Artin stacks.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Combinatorial Mathematics
Advanced Algebra and Geometry
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 1
- Pages
- 71–154
- Publication date
- 19 January 2026
- Language
- EN