Log canonical models of foliated surfaces

2021/03/23 by Yenan Chen, Chen, Yen-An
Mathematics · #14D20 #14E99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Primary 32M25 #Secondary 14C20

paper · pdf · doi:10.48550/arxiv.2103.12669

openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of separatedness and properness and a property related to local-closedness for the moduli functor S_P^sm which parametrizes the stable smoothable foliated surface pairs. On the way, we also show a result on the invariance of plurigenera.

Related

• Failure of Boundedness for Generalised Log Canonical Surfaces
• Log canonical foliation singularities on surfaces
• ACC for foliated log canonical thresholds
• Canonical Models of Adjoint Foliated Structures on Surfaces
• Adjoint log canonical foliated singularities on surfaces