Stable Reduction via the Log Canonical Model

2024/11/26 by Chung, Tai-Hsuan
Mathematics · #14D06 #14E30 #14G17 #14J17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2411.17909

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model Program. As a result, we recover the Hacon-Kovács theorem on the properness of the moduli stack \mathscrM_2,v,k of stable surfaces of volume v defined over k=k, provided that chark>C(v), a constant depending only on v.

Related

• On the properness of the moduli space of stable surfaces over ℤ[1/30]
• Log canonical singularities and complete moduli of stable pairs
• Stratified Hyperbolicity of the moduli stack of stable minimal models, I
• Log minimal model program for the moduli space of stable curves: The second flip
• Hyperbolicity of the base of an admissible family of log canonical stable minimal models