What question did this study set out to answer?

This research aims to explore the application of minimal model theory for log surfaces within the analytic context.

April 12, 2026Open Access

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

Key Points

This research aims to explore the application of minimal model theory for log surfaces within the analytic context.
Discussion of the minimal model program
Examination of the abundance theorem
Analysis of log canonical rings for log pairs
Application to complex surfaces that are projective over analytic varieties
Validation of the minimal model program for log pairs of complex surfaces
Confirmation of the abundance theorem's applicability
Establishment of finite generation of log canonical rings

Abstract

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.

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Cite This Study

Nao Moriyama (Thu,) studied this question.

synapsesocial.com/papers/69db37254fe01fead37c5162 https://doi.org/https://doi.org/10.1017/nmj.2026.10108

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