Szilard Szabo: The oper stratification and apparent singularities

Kivonat: After a short discussion of the Hodge moduli space of a complex projective curve, we describe a recent construction of C. Simpson for holomorphic connections on complex projective curves, which leads to a stratification of the de Rham moduli space. Then we discuss the extension of these results to quasi-projective curves with parabolic structure. Finally, we sketch a conjectural link to apparent singularities of differential equations.