2017 / December Volume 12 No.4
Characterizing projective spaces for varieties with at most quotient singularities
| Published Date |
2017 / December
|
|---|---|
| Title | Characterizing projective spaces for varieties with at most quotient singularities |
| Author | |
| Keyword | |
| Download | |
| Pagination | 297-314 |
| 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 $X \cong
\mathbb{P}^n$.
|
| DOI | |
| AMS Subject Classification |
14D06, 14D23, 14E08, 14J40, 14J17
|
| Received |
2017-09-11
|
| Accepted |
2017-11-24
|