Higher Codimensional Alpha Invariants and Characterization of Projective Spaces

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.

arXiv comment14 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

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Cited by in corpus (2)

• Birational superrigidity is not a locally closed property
• Noether-Fano Inequalities and Canonical Thresholds on Fano Varieties