Finiteness of log abundant log canonical pairs in log minimal model program with scaling

2020/05/25 by Kenta Hashizume, Hashizume, Kenta · 1 citation
Computer Science · Mathematics · #14E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complexity and Algorithms in Graphs #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2005.12253

openalex publication_date 2020/05/25 · openalex created_date 2020/05/29 · openalex updated_date 2026/07/28

Abstract

We study relations between the property of being log abundant for lc pairs and the termination of log MMP with scaling. We prove that any log MMP with scaling of an ample divisor starting with a projective dlt pair contains only finitely many log abundant dlt pairs. We also discuss log MMP for slc pairs.

Citations

• On Finiteness of B-representation and Semi-log Canonical Abundance
• Remarks on special kinds of the relative log minimal model program

Cited by

• On finiteness of relative log pluricanonical representations

Related

• On minimal model theory for log abundant lc pairs
• An abundance theorem for generalised pairs
• The LMMP for log canonical 3-folds in char p
• Relations between two log minimal models of log canonical pairs
• Introduction to the log minimal model program for log canonical pairs