Logarithmic Kodaira-Akizuki-Nakano vanishing and Arakelov-Parshin boundedness for singular varieties

2000/03/03 by Sándor J. Kovács, Kovács, Sándor J. · 1 citation
Mathematics · #14D06 #14F17 #Advanced Harmonic Analysis Research #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0003019

openalex publication_date 2000/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The article has two parts. The first part is devoted to proving a singular version of the logarithmic Kodaira-Akizuki-Nakano vanishing theorem of Esnault and Viehweg. This is then used to prove other vanishing theorems. In the second part these vanishing theorems are used to prove an Arakelov-Parshin type boundedness result for families of canonically polarized varieties with rational Gorenstein singularities.

Cited by

• On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds

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