Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds

Abstract

This note is written for the Festschrift in honor of Professor Christer Kiselman. Multiplier ideal sheaves identify the location and the extent of the failure of crucial estimates. In this note we will discuss and explain the historic evolution of the notion of multiplier ideal sheaves, especially the interpretation from the viewpoint of destabilizing subsheaves in the context of terminating or bounding an infinite process. We will also discuss the approach of constructing rational curves in Fano manifolds by using dynamic multiplier ideal sheaves and singularity-magnifying complex Monge-Ampere equations. This approach is still under development with details in the process of being worked out. We will indicate where details still need to be worked out.

References in corpus (5)

• Existence of minimal models for varieties of log general type
• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Effective Termination of Kohn's Algorithm for Subelliptic Multipliers
• Additional Explanatory Notes on the Analytic Proof of the Finite Generation of the Canonical Ring
• Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring

Cited by in corpus (1)

• Multiplier ideal sheaves and geometric problems