Degenerations of bundle moduli

Over a family X of complete curves genus g, which gives the degeneration smooth curve into one with nodal singularities, we build moduli space is holomorphic SL(n,C) bundles over generic Xt in family, and equipped extra structure at nodes for family. This quotient by (C⁎)s on desingularization. Taking “maximal” built from glueing three-pointed spheres, obtain (C⁎)(3g−3)(n−1)-quotient (2g−2)-th power associated to sphere. Via Narasimhan-Seshadri theorem, representations fundamental group SU(n) (the “symplectic picture”). We degenerations also this symplectic context, way that compatible degeneration, so our limit (S1)(3g−3)(n−1)