On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow

TL;DR

This paper constructs Nadel multiplier ideal sheaves via Ricci flow on Fano manifolds, extending previous results and providing criteria for the existence of Kähler-Einstein metrics.

Contribution

It introduces a new method of constructing Nadel multiplier ideal sheaves using Ricci flow, broadening the tools for studying Kähler-Einstein metrics.

Findings

Constructed Nadel multiplier ideal sheaves with Ricci flow.

Extended previous results by Phong, Sesum, and Sturm.

Provided an existence criterion for Kähler-Einstein metrics.

Abstract

In this note we construct Nadel multiplier ideal sheaves using the Ricci flow on Fano manifolds. This extends a result of Phong, Sesum and Sturm. These sheaves, like their counterparts constructed by Nadel for the continuity method, can be used to obtain an existence criterion for Kahler-Einstein metrics.