Logarithmic Cartan geometry on complex manifolds

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.2010 Mathematics Subject Classification. 53A15; 53A55; 58A32.

Developing Module for Two-Dimensional Course Based on Ethnomathematics for Fourth Grade of Elementary School Student

“…Geometry is a a branch of Mathematics concerned with shapes, lines, points, spaces and also deals with how to connect certain form and pattern such as angle, length, width, and volume (Biswas, Dumitrescu, & McKay, 2020;Yang & Wang, 2017). Geometry lesson aims in studying a property of shapes and spaces, drawing a various forms of shape (Nur'aini, Harahap, Badruzzaman, & Darmawan, 2017) and it aims in enforcing student's critical thinking as well as responsibility in completing the assignments (Verner, Massarwe, & Bshouty, 2019;Wares & Elstak, 2018).…”