LOGARITHMIC CARTAN GEOMETRY ON COMPLEX MANIFOLDS

Indranil Biswas (1) , Sorin Dumitrescu (2) , Benjamin Mckay (3)

1 TIFR - Tata Institute for Fundamental Research
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 UCC - University College Cork

We pursue the study of holomorphic Cartan geometry with singularities. We introduce the notion of logarithmic Cartan geometry on a complex manifold, with polar part supported on a normal crossing divisor. In particular, we show that the push-forward of a Cartan geometry constructed using a finite Galois ramified covering is a logarithmic Cartan geometry (the polar part is supported on the ramification locus). We also study the specific case of the logarithmic Cartan geometry with the model being the complex affine space.

Domaines: Mathématiques [math]

Indranil Biswas, Sorin Dumitrescu, Benjamin Mckay. LOGARITHMIC CARTAN GEOMETRY ON COMPLEX MANIFOLDS. Journal of Geometry and Physics, In press, 148. ⟨hal-02277614⟩