Kähler cone-manifolds arising from a projective arrangement

Abstract

Given a hyperplane arrangement of some type in a projective space, the Dunkl system, developed by Couwenberg, Heckman and Looijenga, is used to study the geometric structures on its complement, and as a consequence it leads to the discovery of new ball quotients when the so-called Schwarz conditions are imposed. In this talk, I will show that the space, investigated in this system, is still of a particular type of structure, namely, the structure of a cone-manifold, when there are no Schwarz conditions imposed. I will illustrate this theory by discussing the one-dimensional example, which originates from the classical hypergeometric system.

Speaker Intro

Dali Shen is an assistant professor at BIMSA currently. His research is focused on algebraic geometry and complex geometry. He obtained his PhD from Utrecht University. Before joining BIMSA, he held postdoc positions at IMPA and TIFR.