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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2601.03761 |
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| _version_ | 1866915793714806784 |
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| author | Huang, Zhenxi Wang, Shuo Xu, Bin |
| author_facet | Huang, Zhenxi Wang, Shuo Xu, Bin |
| contents | Freed (arXiv:hep-th/9712042) formulated special Kähler structures; in particular, the regular locus of the $\mathrm{SL}_2(\mathbb{C})$ Hitchin base $\mathcal{B}$ carries such a structure, while the associated metric $ω_{\mathrm{SK}}$ is singular along the discriminant locus $\mathcal{D}$. Baraglia-Huang (arXiv:1707.04975) computed its Taylor expansion near points of $\mathcal{B}\setminus\mathcal{D}$. Hitchin (arXiv:1712.09928) then defined subsystems attached to those components of $\mathcal{D}$ whose spectral curves have only nodal singularities; these components form smooth strata with induced special Kähler structures. We show that near such a stratum the canonical special Kähler metric has logarithmic asymptotics in transversal directions, whereas its tangential part converges to a metric on the stratum agreeing with the one from Hitchin's subsystems. Along any complex line through the origin of $\mathcal{B}$ and a point of the stratum, the metric restricts to a cone flat metric with cone angle $π$ at the origin only. Finally, the special Kähler potential extends continuously to these strata, and is $C^1$ on a portion of them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local Models for Special Kähler Metric Singularities Along the Discriminant Locus of the $\mathrm{SL}_2(\mathbb{C})$ Hitchin Base Huang, Zhenxi Wang, Shuo Xu, Bin Differential Geometry Freed (arXiv:hep-th/9712042) formulated special Kähler structures; in particular, the regular locus of the $\mathrm{SL}_2(\mathbb{C})$ Hitchin base $\mathcal{B}$ carries such a structure, while the associated metric $ω_{\mathrm{SK}}$ is singular along the discriminant locus $\mathcal{D}$. Baraglia-Huang (arXiv:1707.04975) computed its Taylor expansion near points of $\mathcal{B}\setminus\mathcal{D}$. Hitchin (arXiv:1712.09928) then defined subsystems attached to those components of $\mathcal{D}$ whose spectral curves have only nodal singularities; these components form smooth strata with induced special Kähler structures. We show that near such a stratum the canonical special Kähler metric has logarithmic asymptotics in transversal directions, whereas its tangential part converges to a metric on the stratum agreeing with the one from Hitchin's subsystems. Along any complex line through the origin of $\mathcal{B}$ and a point of the stratum, the metric restricts to a cone flat metric with cone angle $π$ at the origin only. Finally, the special Kähler potential extends continuously to these strata, and is $C^1$ on a portion of them. |
| title | Local Models for Special Kähler Metric Singularities Along the Discriminant Locus of the $\mathrm{SL}_2(\mathbb{C})$ Hitchin Base |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.03761 |