Higher Codimensional Alpha Invariants and Characterization of Projective Spaces
Algebraic Geometry
2020-01-28 v2
Abstract
We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano manifolds in terms of higher codimensional alpha invariants. Our results demonstrate the relation between alpha invariants of any codimension and volumes of Fano manifolds in the characterization of projective spaces.
Cite
@article{arxiv.1805.07330,
title = {Higher Codimensional Alpha Invariants and Characterization of Projective Spaces},
author = {Ziwen Zhu},
journal= {arXiv preprint arXiv:1805.07330},
year = {2020}
}
Comments
14 pages. Second version: deleted Proposition 3.7 due to a gap in the proof and modified corresponding statements throughout the article. To appear in Internat. J. Math