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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