Birational complexity and dual complexes

2024/02/15 by Mirko Mauri, Mauri, Mirko, Joaquí­n Moraga +1
Chemistry · #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #History and advancements in chemistry #Primary 14E05 #Secondary 57Q05

paper · pdf · doi:10.48550/arxiv.2402.10136

openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We introduce the notion of birational complexity of a log Calabi-Yau pair. This invariant measures how far the log Calabi-Yau pair is to being birational to a toric pair. We study fundamental properties of the new invariant, with a particular focus on the geometry of dual complexes.

Related

• Log Calabi-Yau pairs of birational complexity zero
• Birational complexity and conic fibrations
• Log Calabi--Yau pairs of complexity zero and arbitrary index
• Birational complexity of log Calabi-Yau 3-folds
• Generalized complexity of surfaces