A logarithmic ∂-equation on a compact Kähler manifold associated to a smooth divisor

2018/05/30 by Xueyuan Wan, Wan, Xueyuan
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1805.11920

openalex publication_date 2018/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we solve a logarithmic ∂-equation on a compact Kähler manifold associated to a smooth divisor by using the cyclic covering trick. As applications, we discuss the closedness of logarithmic forms, injectivity theorems and obtain a kind of degeneration of spectral sequence at E₁, and we also prove that the pair (X,D) has unobstructed deformations for any smooth divisor D∈|-2K_X|.

Citations

• Introduction to the log minimal model program for log canonical pairs
• Solving equations with Hodge theory

Related

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• Geometry of logarithmic forms and deformations of complex structures
• Logarithmic vanishing theorems on compact Kähler manifolds I
• Solutions of the ∂ -equation on Stein and on Kähler manifold with compact support
• Logarithmic vanishing theorems for effective q-ample divisors