(Quasi-)affineness of perverse character varieties
We show that perverse character varieties are (quasi-)affine. We do this in a purely stack-theoretic fashion, by exhibiting enough sections of the structure sheaf.
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arXiv subjects
Enrico Lampetti
Publications and source records attributed to Enrico Lampetti.
Lagrangian structures on the derived moduli of constructible sheaves
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.
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Good moduli for moduli of objects
We construct good moduli spaces from moduli of objects in the sense of Toën-Vaquié. As an application, we construct good moduli spaces for perverse sheaves.
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Good moduli space for constructible sheaves and Stokes functors
In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.
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