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arXiv:math.DG/0402316v119Feb2004 Symmetries, Quotients
 

Summary: arXiv:math.DG/0402316v119Feb2004
Symmetries, Quotients
and
Kšahler-Einstein 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 Kšahler-Einstein metric. Under some nu-
merical and smoothness assumptions on the ramification divisors, we
prove that M admits a Kšahler-Einstein 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 Kšahler-Einstein
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-

  

Source: Arezzo, Claudio - Dipartimento di Matematica, Università degli Studi di Parma

 

Collections: Mathematics