Visible Lagrangians for Hitchin Systems and Pillowcase Covers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914380258476032 |
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| author | Horn, Johannes Schwab, Johannes |
| author_facet | Horn, Johannes Schwab, Johannes |
| contents | We study complex Lagrangians in Hitchin systems that factor through a proper subvariety of the Hitchin base non-trivially intersecting the regular locus. This gives a general framework for several examples in the literature. We compute the fiber-wise Fourier-Mukai transform of flat line bundles on visible Lagrangians. This proposes a construction of mirror dual branes to visible Lagrangians. Finally, we study a new example of visible Lagrangians in detail. Such visible Lagrangian exists whenever the underlying Riemann surface is a pillowcase cover. The proposed mirror dual brane turns out to be closely related to Hausel's toy model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15716 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Visible Lagrangians for Hitchin Systems and Pillowcase Covers Horn, Johannes Schwab, Johannes Algebraic Geometry Geometric Topology We study complex Lagrangians in Hitchin systems that factor through a proper subvariety of the Hitchin base non-trivially intersecting the regular locus. This gives a general framework for several examples in the literature. We compute the fiber-wise Fourier-Mukai transform of flat line bundles on visible Lagrangians. This proposes a construction of mirror dual branes to visible Lagrangians. Finally, we study a new example of visible Lagrangians in detail. Such visible Lagrangian exists whenever the underlying Riemann surface is a pillowcase cover. The proposed mirror dual brane turns out to be closely related to Hausel's toy model. |
| title | Visible Lagrangians for Hitchin Systems and Pillowcase Covers |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2310.15716 |