Birational complexity and conic fibrations

2024/03/25 by Joaquí­n Moraga, Moraga, Joaquín
Computer Science · #14E30 #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14E05 #Secondary 14D06

paper · pdf · doi:10.48550/arxiv.2403.17251

openalex publication_date 2024/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,B) be a log Calabi-Yau pair of dimension n, index one, and birational complexity c. We show that (X,B) has a crepant birational model that admits a tower of Mori fiber spaces of which at least n-c are conic fibrations. Motivated by the proof of the previous statement, we introduce new measures of the complexity of a log Calabi-Yau pair; the alteration complexity and the conic complexity. We characterize when these invariants are zero. Finally, we give applications of the tools of the main theorem to birational superrigidity, Fano hypersurfaces, dual complexes, Weil indices of Fano varieties, and klt singularities.

Related

• Log Calabi-Yau pairs of birational complexity zero
• Birational complexity of log Calabi-Yau 3-folds
• Birational complexity and dual complexes
• Log Calabi--Yau pairs of complexity zero and arbitrary index
• Log Calabi-Yau fibrations