Abstract
A log Calabi–Yau surface with maximal boundary, or Looijenga pair, is a pair (Y,D) with Y a smooth rational projective complex surface and D=D1+⋯+Dl∈|−KY| an anticanonical singular nodal curve. Under some natural conditions on the pair, we propose a series of correspondences relating five different classes of enumerative invariants attached to (Y,D):
1. the log Gromov–Witten theory of the pair (Y,D),
2. the Gromov–Witten theory of the total space of ⊕iOY(−Di),
3. the open Gromov–Witten theory of special Lagrangians in a Calabi–Yau 3–fold determined by (Y,D),
4. the Donaldson–Thomas theory of a symmetric quiver specified by (Y,D), and
5. a class of BPS invariants considered in different contexts by Klemm and Pandharipande, Ionel and Parker, and Labastida, Mariño, Ooguri and Vafa.
We furthermore provide a complete closed-form solution to the calculation of all these invariants.
1. the log Gromov–Witten theory of the pair (Y,D),
2. the Gromov–Witten theory of the total space of ⊕iOY(−Di),
3. the open Gromov–Witten theory of special Lagrangians in a Calabi–Yau 3–fold determined by (Y,D),
4. the Donaldson–Thomas theory of a symmetric quiver specified by (Y,D), and
5. a class of BPS invariants considered in different contexts by Klemm and Pandharipande, Ionel and Parker, and Labastida, Mariño, Ooguri and Vafa.
We furthermore provide a complete closed-form solution to the calculation of all these invariants.
| Original language | English |
|---|---|
| Pages (from-to) | 393–496 |
| Number of pages | 104 |
| Journal | Geometry & Topology |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 27 Feb 2024 |
Bibliographical note
Funding:This project has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement 746554 (van Garrel), the Engineering and Physical Sciences Research Council under grant agreement EP/S003657/2 (Brini) and by Dr Max Rössler, the Walter Haefner Foundation, the ETH Zürich Foundation, and the NSF grant DMS-2302117 (Bousseau).
Keywords
- Gromov–Witten invariants
- mirror symmetry
- log Calabi–Yau surfaces
- Donaldson–Thomas invariants