On the generalized Futaki invariant

TL;DR

This paper investigates the algebraic structure of the generalized Futaki invariant for almost Fano varieties, demonstrating its computation via equivariant Chow cohomology and Bott-type formulas with illustrative examples.

Contribution

It establishes that the generalized Futaki invariant can be expressed as a pushforward of an equivariant Chow cohomology class, enabling new computational methods.

Findings

The invariant is a pushforward of an equivariant Chow class.

Bott-type formulas can be applied to compute the invariant.

Examples illustrate the practical computation of the invariant.

Abstract

We study the algebraic properties of the generalized Futaki invariant of an almost Fano variety and prove that it is in fact a pushforward to a point of an appropriate equivariant Chow cohomology class of the variety. This allows us to use Bott-type formulae for calculating the invariant. We show this use on some examples.