2016/08/02 by Indranil Biswas, Biswas, Indranil, Viktoria Heu +3
Mathematics · #16h40 #53B15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:16h40 #msc:53B15
paper · pdf · doi:10.48550/arxiv.1608.00780
arxiv created 2016/08/02 · arxiv updated 2016/08/03
Let G be a reductive affine algebraic group defined over \mathbb C, and let ∇0 be a meromorphic G-connection on a holomorphic G-bundle E0, over a smooth complex curve X0, with polar locus P0 ⊂ X0. We assume that ∇0 is irreducible in the sense that it does not factor through some proper parabolic subgroup of G. We consider the universal isomonodromic deformation (Et→ Xt, ∇t, Pt)t∈ T of (E0→ X0, ∇0, P0), where T is a certain quotient of a certain framed Teichmüller space we describe. We show that if the genus g of X0 satisfies g≥ 2, then for a general parameter t∈ T, the G-bundle Et→ Xt is stable. For g≥ 1, we are able to show that for a general parameter t∈ T, the G-bundle Et→ Xt is semistable.