On K-stability of Fano weighted hypersurfaces

2021/11/30 by Sano, Taro, Tasin, Luca · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.15209

Abstract

Let X ⊂ \mathbb P(a₀,…,a_n) be a quasi-smooth weighted Fano hypersurface of degree d and index I_X such that a_i |d for all i, with a₀ ≤ … ≤ a_n. If I_X=1, we show that, under a suitable condition, the α-invariant of X is greater than or equal to dim X/(dim X+1) and X is K-stable. This can be applied in particular to any X as above such that dim X ≤ 3. If X is general and I_X < dim X, then we show that X is K-stable. We also give a sufficient condition for the finiteness of automorphism groups of quasi-smooth Fano weighted complete intersections.

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