On the modified Futaki invariant of complete intersections in projective spaces

DOI10.1017/NMJ.2016.16zbMATH Open1351.53060arXiv1410.4891OpenAlexW2265409204MaRDI QIDQ2828017

Ryosuke Takahashi

Publication date: 24 October 2016

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Abstract: It is known that a necessary condition for the existence of K"ahler-Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian-Zhu. In a recent work of Berman-Nystr"om, it was generalized for (singular) Fano varieties and the notion of algebro-geometric stability of the pair $(M,V)$ of a Fano manifold $M$ and a holomorphic vector field $V$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

Full work available at URL: https://arxiv.org/abs/1410.4891

zbMATH Keywords

Fano varietycomplete intersectionKähler-Ricci soliton

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Fano varieties (14J45) Moduli, classification: analytic theory; relations with modular forms (14J15)

Related Items (3)

Asymptotic stability for Kähler-Ricci solitons ⋮ [[Publication:3697156|Title not available (Why is that?)]] ⋮ The Futaki invariant and the Mabuchi energy of a complete intersection

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