ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES

2014/10/31 by Ryosuke Takahashi · 1 citation
Mathematics · Physics and Astronomy · #Fano plane #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic function #Invariant (physics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Projective space #Projective test #Pure mathematics #math.DG #msc:53C25

paper · pdf · doi:10.1017/nmj.2016.16

published in Nagoya Mathematical Journal 222(1), 186-209 (Cambridge University Press) · 17 pages, final version, to appear in Nagoya Mathematical Journal

openalex publication_date 2016/06/01 · arxiv created 2016/06/09 · arxiv updated 2016/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let M be a Fano manifold. We call a Kähler metric \itω∈ c₁(M) a Kähler–Ricci soliton if it satisfies the equation Ric(\itω)-\itω=L_V\itω for some holomorphic vector field V on M . It is known that a necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian and Zhu. In a recent work of Berman and Nyström, it was generalized for (possibly singular) Fano varieties, and the notion of algebrogeometric stability of the pair (M,V) was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

Citations

• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Heat Kernels and Dirac Operators
• K-stability and Kähler-Einstein metrics
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof