Birational geometry of Calabi-Yau pairs (ℙ³, D) of coregularity 2

2024/02/21 by Eduardo Alves da Silva, da Silva, Eduardo Alves
Mathematics · #14E05 #14E07 (Primary) 14E30 #14J17 #14J30 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2402.13970

openalex publication_date 2024/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper aims to study the birational geometry of log Calabi-Yau pairs(ℙ³, D) of coregularity 2, where in this case D is an irreducible normal quartic surface with canonical singularities. We completely classify which toric weighted blowups of a point will initiate a volume preserving Sarkisov link starting with this pair. Depending on the type of singularity, our results point out that some of these weights do not work generically for a general member of the corresponding coarse moduli space of quartics.

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