Quasimaps and stable pairs
We prove an equivalence between the Bryan-Steinberg theory of $\pi $-stable pairs on $Y = \mathcal {A}_{m-1} \times \mathbb {C}$ and the theory of quasimaps to $X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2021-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509421000256/type/journal_article |
| Summary: | We prove an equivalence between the Bryan-Steinberg theory of $\pi $-stable pairs on
$Y = \mathcal {A}_{m-1} \times \mathbb {C}$ and the theory of quasimaps to
$X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of both vertices are described explicitly via box counting. Then we apply the equivalence to study the implications for sheaf-counting theories on Y arising from 3D mirror symmetry for quasimaps to X, including the Donaldson-Thomas crepant resolution conjecture. |
|---|---|
| ISSN: | 2050-5094 |