基于循环覆盖与L2方法的q-丰沛除子对数消灭定理的研究
Logarithmic Vanishing Theorems for q-Ample Divisors via Cyclic Coverings and L2 Method
DOI: 10.12677/pm.2025.159227, PDF,    国家自然科学基金支持
作者: 郭坤燕：重庆理工大学数学科学学院，重庆；万学远：重庆理工大学数学科学研究中心，重庆
关键词: 对数消灭定理；循环覆盖；q-丰沛除子；紧Kähler流形；Log Vanishing Theorem； Cyclic Covering； q-Ample Divisor； Compact Kähler Manifold
摘要: 本文主要使用循环覆盖技巧与L2方法来研究紧Kähler流形上q-丰沛除子的对数消灭定理。首先回顾了对数微分形式层及带有对数可积联络的层的基本理论。随后利用循环覆盖技巧，证明了紧Kähler流形上支撑于q-丰沛除子的光滑除子及简单交叉除子的若干新的对数消灭定理。
Abstract: This paper primarily employs the technique of cyclic covering and L2 method to investigate logarithmic vanishing theorems for q-ample divisors on compact Kähler manifolds. We begin by reviewing the foundational theory of logarithmic differential forms and sheaves equipped with logarithmic integrable connections. Building on this, we apply the cyclic covering method to establish several new logarithmic vanishing theorems for smooth divisors and simple normal crossing divisors supported on q-ample divisors in the compact Kähler setting.
文章引用：郭坤燕, 万学远. 基于循环覆盖与L2方法的q-丰沛除子对数消灭定理的研究[J]. 理论数学, 2025, 15(9): 1-9. https://doi.org/10.12677/pm.2025.159227

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