K-polystability of two smooth Fano threefolds

2021/07/10 by Ivan Cheltsov, Cheltsov, Ivan, Hendrik Süß +1
Mathematics · #14J45 #32Q20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2107.04797

openalex publication_date 2021/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give new proofs of the K-polystability of two smooth Fano threefolds. One of them is a~smooth divisor in ℙ¹×ℙ¹×ℙ² of degree (1,1,1), which is unique up to isomorphism. Another one is the~blow up of the complete intersection \x₀x₃+x₁x₄+x₂x₅=x₀²+ωx₁²+ω²x₂²+(x₃²+ωx₄²+ω²x₅²)+(x₀x₃+ωx₁x₄+ω²x₂x₅)\⊂ℙ⁵ in the conic cut out by x₀=x₁=x₂=0, where ω is a~primitive cube root of unity.

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