Mysterious duality and helical line bundles on del Pezzo surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913939946733568 |
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| author | King, Alastair |
| author_facet | King, Alastair |
| contents | Mysterious duality is a relationship, described by Vafa in 2000, between $\frac12$-BPS branes in Type II supergravity in dimension $D=d+2$ and rational curves on del Pezzo surfaces of degree $d$. We show that both sides of this correspondence can be linked to a $\mathbb{Z}_d$ grading of the Lie algebra $E_8$. In addition, we show that the relevant rational curves correspond to `helical' line bundles, that is, line bundles that can appear in a helix on the del Pezzo surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mysterious duality and helical line bundles on del Pezzo surfaces King, Alastair Algebraic Geometry 14F26 Mysterious duality is a relationship, described by Vafa in 2000, between $\frac12$-BPS branes in Type II supergravity in dimension $D=d+2$ and rational curves on del Pezzo surfaces of degree $d$. We show that both sides of this correspondence can be linked to a $\mathbb{Z}_d$ grading of the Lie algebra $E_8$. In addition, we show that the relevant rational curves correspond to `helical' line bundles, that is, line bundles that can appear in a helix on the del Pezzo surface. |
| title | Mysterious duality and helical line bundles on del Pezzo surfaces |
| topic | Algebraic Geometry 14F26 |
| url | https://arxiv.org/abs/2507.10169 |