Singularities and K-semistability

TL;DR

This paper extends the Futaki invariant to big and nef classes, providing new tools for checking K-semistability and improving bounds on Calabi energy, with implications for singularities and stability in algebraic geometry.

Contribution

It introduces a continuous Futaki invariant for big and nef classes and shows reduced normal crossing singularities suffice for K-semistability checks.

Findings

Futaki invariant extended to big and nef classes.

Reduced normal crossing singularities suffice for K-semistability.

Improved lower bound for Calabi energy.

Abstract

In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities are sufficient to check $K$-semistability. A similar improvement on Donaldson's lower bound for Calabi energy is given.