A remark on the Moduli of parabolic connections

Abstract

We consider the moduli space of stable parabolic connections of full flag type with generic rational weights on a compact Riemann surface $X$ of genus $g\ge 3$, with singularities along the parabolic points. We compute the Chow groups of the fixed determinant moduli space consisting of parabolic connections whose underlying parabolic bundle is stable. We show that the moduli space of stable parabolic connections is not rationally connected, whereas the fixed determinant moduli space is rationally connected and in fact rational. We also prove that the determinant map to the Picard variety is universal among morphisms to abelian varieties. Finally, we show that the algebraic group of rank one holomorphic connections acts trivially on the cohomology of the moduli space of stable parabolic connections.

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