Lagrangian structures on the derived moduli of constructible sheaves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910042268106752 |
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| author | Christ, Merlin Lampetti, Enrico |
| author_facet | Christ, Merlin Lampetti, Enrico |
| contents | Given a compact oriented manifold of dimension $n$ with a conically smooth stratification, we show that the moduli of $\mathcal{D}(k)$-valued constructible sheaves and the moduli of perverse sheaves are $(2-n)$-shifted Lagrangian. The former statement follows from the construction of a relative left $n$-Calabi--Yau structure on the stable $\infty$-category of $\mathcal{D}(k)$-valued constructible sheaves. This is achieved via a lax gluing result for categorical cubes equipped with cubical Calabi--Yau structures. Given a codimension $2$ submanifold, we further identify symplectic leaves corresponding to perverse sheaves with prescribed monodromy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_04983 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lagrangian structures on the derived moduli of constructible sheaves Christ, Merlin Lampetti, Enrico Algebraic Geometry Algebraic Topology 32S60 (Primary) 14D23, 18N60 (Secondary) Given a compact oriented manifold of dimension $n$ with a conically smooth stratification, we show that the moduli of $\mathcal{D}(k)$-valued constructible sheaves and the moduli of perverse sheaves are $(2-n)$-shifted Lagrangian. The former statement follows from the construction of a relative left $n$-Calabi--Yau structure on the stable $\infty$-category of $\mathcal{D}(k)$-valued constructible sheaves. This is achieved via a lax gluing result for categorical cubes equipped with cubical Calabi--Yau structures. Given a codimension $2$ submanifold, we further identify symplectic leaves corresponding to perverse sheaves with prescribed monodromy. |
| title | Lagrangian structures on the derived moduli of constructible sheaves |
| topic | Algebraic Geometry Algebraic Topology 32S60 (Primary) 14D23, 18N60 (Secondary) |
| url | https://arxiv.org/abs/2603.04983 |