Characterizing projective spaces for varieties with at most quotient singularities
by
Jiun Cheng Chen
Vol. 12 No. 4 (2017) P.297~P.314
DOI: | https://doi.org/10.21915/BIMAS.2017401 |
| 10.21915/BIMAS.2017401 |
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 $X \cong
\mathbb{P}^n$.
KEYWORDS
Projective space, quotient singularity, pseudo-index, deformation theory, twisted stable curves
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 14D06, 14D23, 14E08, 14J40, 14J17
MILESTONES
Received: 2017-09-11
Revised :
Accepted: 2017-11-24
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