Abstract
Let G be a finite subgroup of SUp4q such that its elements have age
at most one. In the first part of this paper, we define K-theoretic stable pair
invariants on a crepant resolution of the affine quotient C4{G, and conjecture
a closed formula for their generating series in terms of the root system of G. In
the second part, we define degree zero Donaldson-Thomas invariants of CalabiYau 4-orbifolds, develop a vertex formalism that computes the invariants in
the toric case, and conjecture closed formulae for their generating series for
the quotient stacks rC4{Zrs, rC4{Z2 ˆ Z2s. Combining these two parts, we
formulate a crepant resolution correspondence which relates the above two
theories.
at most one. In the first part of this paper, we define K-theoretic stable pair
invariants on a crepant resolution of the affine quotient C4{G, and conjecture
a closed formula for their generating series in terms of the root system of G. In
the second part, we define degree zero Donaldson-Thomas invariants of CalabiYau 4-orbifolds, develop a vertex formalism that computes the invariants in
the toric case, and conjecture closed formulae for their generating series for
the quotient stacks rC4{Zrs, rC4{Z2 ˆ Z2s. Combining these two parts, we
formulate a crepant resolution correspondence which relates the above two
theories.
| Original language | English |
|---|---|
| Pages (from-to) | 8225-8268 |
| Number of pages | 44 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 376 |
| Issue number | 11 |
| Early online date | 1 Sept 2023 |
| DOIs | |
| Publication status | Published - Nov 2023 |
Bibliographical note
Publisher Copyright:© 2023 American Mathematical Society.
Funding
Received by the editors March 5, 2023, and, in revised form, July 1, 2023. 2020 Mathematics Subject Classification. Primary 14N35, 14C05. The first author was partially supported by RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), JSPS KAKENHI Grant Number JP19K23397 and Royal Society Newton International Fellowships Alumni 2021 and 2022. The second author was supported by NWO grant VI.Vidi.192.012. The third author was partially supported by NWO grant TOP2.17.004 and the Chair of Arithmetic Geometry, EPFL.
| Funders | Funder number |
|---|---|
| Royal Society | |
| Japan Society for the Promotion of Science | JP19K23397 |
| École Polytechnique Fédérale de Lausanne | |
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | TOP2.17.004, VI.Vidi.192.012 |
| RIKEN |