On termination of minimal model program for log canonical pairs on complex analytic spaces

TL;DR

This paper investigates the termination of minimal model programs for log canonical pairs in complex analytic spaces, establishing connections with algebraic and stack settings.

Contribution

It extends minimal model program termination results to complex analytic spaces and explores implications for algebraic and stack contexts.

Findings

Proves termination of minimal model programs in complex analytic setting.

Establishes relations between algebraic and analytic minimal model theories.

Discusses minimal model programs for algebraic and analytic stacks.

Abstract

We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log canonical pairs in the complex analytic setting. The minimal model programs for algebraic stacks and analytic stacks are also discussed.