 
Summary: arXiv:math.DG/0402316v119Feb2004
Symmetries, Quotients
and
KšahlerEinstein metrics
Claudio Arezzo, Alessandro Ghigi, Gian Pietro Pirola
February 20, 2004
Abstract
We consider Fano manifolds M that admit a collection of finite auto
morphism groups G1, ..., Gk, such that the quotients M/Gi are smooth
Fano manifolds possessing a KšahlerEinstein metric. Under some nu
merical and smoothness assumptions on the ramification divisors, we
prove that M admits a KšahlerEinstein metric too.
Contents
1 Introduction 1
2 Existence theorems on covering spaces 4
3 Examples 23
1 Introduction
The aim of this paper is to provide new examples of KšahlerEinstein
metrics of positive scalar curvature. The existence of such a metric
on a Fano manifold is a subtle problem, due to the presence of ob
