Hyperpolygons and parabolic Higgs bundles

Speaker: Alessia Mandini, PUC-Rio.

Date: 07 jun 2019, 11h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: Hyperpolygons spaces are a family of (finite dimensional, non-compact) hyperkaehler spaces, that can be obtained from coadjoint orbits by hyperkaehler reduction. Jointly with L. Godinho, we show that these space are diffeomorphic (in fact, symplectomorphic) to certain families of parabolic Higgs bundles. In this talk, I will describe this relation and use it to analyze the fixed points locus of a natural involution on the moduli space of parabolic Higgs bundles. I will show that each connected component of the fixed point locus of this involution is identified with a moduli space of polygons in Minkowski 3-space.

This is based on

  • L.Godinho, A. Mandini, "Hyperpolygon spaces and moduli spaces of parabolic Higgs bundles" Adv. Math. 244 (2013), 465–532
  • I.Biswas, C.Florentino, L.Godinho, A.Mandini, "Polygons in the Minkowski three space and parabolic Higgs bundles of rank two on CP^1, Transfom. Groups 18 (2013)
  • I.Biswas, C.Florentino, L.Godinho, A.Mandini, "symplectic form on hyperpolygon space", Geom. Dedicata 179 (2015)