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Lazarsfeld, R. (2003) Positivity in Algebraic Geometry. II. Positivity for Vector Bundles, and Multiplier Ideals. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, 49.

has been cited by the following article:

• TITLE: Invariance of Plurigenera in Smooth Projective Families: An Algebraic Approach

  AUTHORS: Jie Huang

  KEYWORDS: Algebraic Proof, Invariance of Plurigenera, Multiplier Ideal Sheaves, Nadel Vanishing Theorem

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 7, 2025

  ABSTRACT: This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations. While Siu’s original proof relied on analytic tools such as multiplier ideal sheaves and L 2 -extension theorems, our approach reformulates these techniques within the framework of algebraic geometry, emphasizing multiplier ideals, Castelnuovo-Mumford regularity, and Nadel vanishing theorem. Key steps include establishing the surjectivity of restriction maps for pluricanonical sections via careful analysis of base ideals and asymptotic multiplier ideals. This work aligns with recent efforts to translate Siu’s results into algebraic settings and provides a foundation for extending the invariance theorem to singular varieties.