Conifold gap and all-genus mirror symmetry for local $\mathbb{P}^2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912629119778816 |
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| author | Brini, Andrea |
| author_facet | Brini, Andrea |
| contents | The Conifold Gap Conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes $G$-function. In this paper, I prove the Conifold Gap Conjecture for the local projective plane. The proof relates the higher genus conifold Gromov-Witten generating series of local $\mathbb{P}^2$ to the thermodynamics of a certain statistical mechanical ensemble of repulsive particles on the positive half-line. As a corollary, this establishes the all-genus mirror principle for local $\mathbb{P}^2$ through the direct integration of the BCOV holomorphic anomaly equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conifold gap and all-genus mirror symmetry for local $\mathbb{P}^2$ Brini, Andrea Algebraic Geometry High Energy Physics - Theory Mathematical Physics The Conifold Gap Conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes $G$-function. In this paper, I prove the Conifold Gap Conjecture for the local projective plane. The proof relates the higher genus conifold Gromov-Witten generating series of local $\mathbb{P}^2$ to the thermodynamics of a certain statistical mechanical ensemble of repulsive particles on the positive half-line. As a corollary, this establishes the all-genus mirror principle for local $\mathbb{P}^2$ through the direct integration of the BCOV holomorphic anomaly equations. |
| title | Conifold gap and all-genus mirror symmetry for local $\mathbb{P}^2$ |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2509.19298 |