Poisson geometry of the moduli of local systems on smooth varieties
arXiv:1809.03536
The paper investigates moduli spaces of G‑local systems on smooth complex algebraic varieties (not necessarily proper), showing that as derived algebraic stacks they naturally carry Poisson structures and describing their symplectic leaves via fixed monodromies at infinity, with a new strictness condition arising from crossing divisors.
Abstract
We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably 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 non-trivial crossings.
31 pages, minor corrections