Relations between two log minimal models of log canonical pairs

TL;DR

This paper investigates the relationships between different log minimal models of a fixed log canonical pair, showing they can be connected via flops and sharing certain properties, with examples illustrating differences.

Contribution

It proves that two log minimal models of an lc pair can be connected by a sequence of flops and shares properties, advancing understanding of their relationships.

Findings

Log minimal models can be connected by flops.

Two models share some properties.

Examples show models with different properties.

Abstract

We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by a sequence of flops, and the two log minimal models share some properties. We also give examples of two log minimal models of an lc pair which have different properties.