Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

Jiun-Cheng Chen

Characterizing Projective Spaces for Varieties with at Most Quotient Singularities

代数几何 2007-05-23 v1

作者: Jiun-Cheng Chen

摘要

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 $X \cong \PP^n$ .

关键词

projective varieties projective geometry algebraic curves

引用

@article{arxiv.math/0604522,
  title  = {Characterizing Projective Spaces for Varieties with at Most Quotient Singularities},
  author = {Jiun-Cheng Chen},
  journal= {arXiv preprint arXiv:math/0604522},
  year   = {2007}
}

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