Birational complexity of log Calabi-Yau 3-folds

2024/05/28 by Joaquí­n Moraga, Moraga, Joaquín
Mathematics · #14J32 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 14E05 #Secondary 14E30

paper · pdf · doi:10.48550/arxiv.2405.18516

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the birational complexity of log Calabi-Yau 3-folds. For such a pair (X,B) of index one and coregularity zero, we show that c_{\rm bir}(X,B)∈ \0,2,3\. Further, we prove that (X,B) has a log Calabi-Yau crepant birational model that admits a crepant contraction to (ℙ^3-c,H₀+…+H_3-c), where c=c_{\rm bir}(X,B). To prove this, we give a geometric characterization of standard ℙ¹-links.

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