Stable maps to Looijenga pairs
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| Format: | Preprint |
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2020
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| _version_ | 1866910354145017856 |
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| author | Bousseau, Pierrick Brini, Andrea van Garrel, Michel |
| author_facet | Bousseau, Pierrick Brini, Andrea van Garrel, Michel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_08830 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stable maps to Looijenga pairs Bousseau, Pierrick Brini, Andrea van Garrel, Michel Algebraic Geometry High Energy Physics - Theory Mathematical Physics 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. |
| title | Stable maps to Looijenga pairs |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2011.08830 |