Multiplier ideal sheaves in complex and algebraic geometry

摘要

This article discusses the geometric application of the method of multiplierideal sheaves. It first briefly describes its application to effective problemsin algebraic geometry and then presents and explains its application to thedeformational invariance of plurigenera for general compact algebraicmanifolds. Finally its application to the conjecture of the finite generationof the canonical ring is explored and the use of complex algebraic geometry incomplex Neumann estimates is discussed.