Remarks on the minimal model theory for log surfaces in the analytic setting

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces which are projective over complex analytic varieties.

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Publication Details

Journal
ArXiv.org
Published
2025-05-23
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Remarks on the minimal model theory for log surfaces in the analytic setting

ArXiv.org
Algebraic Geometry and Number Theory
article

Remarks on the minimal model theory for log surfaces in the analytic setting

article en

Abstract

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of complex surfaces which are projective over complex analytic varieties.

ArXiv.org
Kyoto University (JP)
Openalex Percentile: Top 43%
Algebraic Geometry and Number Theory
Open Access PDFOpenAlex
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Remarks on the minimal model theory for log surfaces in the analytic setting · ArXiv.org (2025) | TGRS Research Map | TGRS