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Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

Jiun-Cheng Chen
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Abstract

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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Jiun-Cheng Chen. 2006-04-25. Characterizing Projective Spaces for Varieties with at Most Quotient Singularities. https://arxiv.org/abs/math/0604522

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