Poisson Geometry of the Moduli of Local Systems on Smooth Varieties
Tony PantevUniversity of Pennsylvania, Philadelphia, USA
Bertrand ToënCNRS, Université de Toulouse, France
We study the moduli of -local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well-known case of curves. We also construct symplectic leaves of this Poisson structure by fixing local monodromies at infinity and show that a new feature, called strictness, appears as soon as the divisor at infinity has nontrivial crossings.
Cite this article
Tony Pantev, Bertrand Toën, Poisson Geometry of the Moduli of Local Systems on Smooth Varieties. Publ. Res. Inst. Math. Sci. 57 (2021), no. 3/4, pp. 959–991DOI 10.4171/PRIMS/57-3-8