Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

Details Characterizing Projective Spaces for Varieties with at Most Quotient Singularities Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

2006-04-25

arxiv.org/abs/math/0604522v1

Mathematics

Algebraic Geometry

Scientific paper

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 $n \geq 3$
with at most quotient singularities. Our result asserts that if $C \cdot (-K_X)
\geq n+1$ for every curve $C \subset X$, then $X \cong \PP^n$.

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