Lagrangian structures on the derived moduli of constructible sheaves

Fuente: arXiv
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Main Authors: Christ, Merlin, Lampetti, Enrico
Format: Preprint
Published: 2026
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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
id 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