Authors: Indranil Biswas ¹; Sorin Dumitrescu ²; Benjamin McKay ³

• 1 Tata Institute for Fundamental Research [TIFR]
• 2 Laboratoire Jean Alexandre Dieudonné
• 3 University College Cork

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.