Poisson Geometry of the Moduli of Local Systems on Smooth Varieties

  • Tony Pantev

    University of Pennsylvania, Philadelphia, USA
  • Bertrand Toën

    CNRS, Université de Toulouse, France
Poisson Geometry of the Moduli of Local Systems on Smooth Varieties cover

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Abstract

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. 959–991

DOI 10.4171/PRIMS/57-3-8