Multiplier ideal sheaves in complex and algebraic geometry

Abstract

This article discusses the geometric application of the method of multiplier ideal sheaves. It first briefly describes its application to effective problems in algebraic geometry and then presents and explains its application to the deformational invariance of plurigenera for general compact algebraic manifolds. Finally its application to the conjecture of the finite generation of the canonical ring is explored and the use of complex algebraic geometry in complex Neumann estimates is discussed.

This article is an expanded version of a talk given on August 23, 2004 in the International Conference on Several Complex Variables in Capital Normal University, Beijing, China and will appear in "Science in China," Series A Mathematics 2005 Volume 48, as part of the proceedings of the conference

References in corpus (1)

• Invariance of Plurigenera

Cited by in corpus (4)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• Finite Generation of Canonical Ring by Analytic Method
• Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces