Shranjeno v:
| Main Authors: | , , |
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| Format: | Preprint |
| Izdano: |
2020
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/2011.08830 |
| Oznake: |
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Kazalo:
- 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 $D=D_1+\dots + D_l \in |-K_Y|$ an anticanonical singular nodal curve. Under some positivity 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 $\bigoplus_i \mathcal{O}_Y(-D_i)$, 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-Pandharipande, Ionel-Parker, and Labastida-Marino-Ooguri-Vafa. We furthermore provide a complete closed-form solution to the calculation of all these invariants.