The 3-fold K-theoretic DT/PT vertex correspondence holds
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918296993923072 |
|---|---|
| author | Kuhn, Nikolas Liu, Henry Thimm, Felix |
| author_facet | Kuhn, Nikolas Liu, Henry Thimm, Felix |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15697 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The 3-fold K-theoretic DT/PT vertex correspondence holds Kuhn, Nikolas Liu, Henry Thimm, Felix Algebraic Geometry 14N35 (Primary) 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. |
| title | The 3-fold K-theoretic DT/PT vertex correspondence holds |
| topic | Algebraic Geometry 14N35 (Primary) |
| url | https://arxiv.org/abs/2311.15697 |