LCK metrics on complex spaces with quotient singularities

Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .

On Exceptional Quotient Singularities

We study four-dimensional and five-dimensional exceptional quotient singularities.

Metrics of positive Ricci curvature on quotient spaces

One of the classical problems in differential geometry is the investigation of closed manifolds which admit Riemannian metrics with given lower bounds for the sectional or the Ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold. Despite many efforts during the past decades, this problem is still far from being...

Local Transformations with Fixed Points on Complex Spaces with Singularities.

with coefficients which are analytic in S. This defines for us a topological space which will be denoted by U. If R is any subset of S then U(R) will denote those points of U whose base points are in R. Now there is a function D(z) analytic and not identically zero in S such that for E denoting the points of S where D vanishes the subset U(E) are possible singularities on U. However, U U(E) = U...

Norms on Quotient Spaces