# Logarithmic Cartan geometry on complex manifolds

## TL;DR

This paper introduces logarithmic Cartan geometry on complex manifolds, extending classical concepts to include singularities along divisors, and explores their properties and specific cases.

## Contribution

It defines logarithmic Cartan geometry with polar parts on divisors and shows how push-forwards of certain geometries produce such structures.

## Key findings

- Push-forward of Galois ramified coverings yields logarithmic Cartan geometries.
- Logarithmic Cartan geometry with affine space as model is studied.
- The framework extends classical Cartan geometry to singular settings.

## Abstract

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.