On explicit birational geometry for weak Fano varieties and polarised Calabi-Yau varieties

2023/01/18 by Minzhe Zhu, Zhu, Minzhe
Mathematics · #14J32 #14J40 #14J45 #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.2301.07462

openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a natural number l and a weak Fano n-fold X with dimφ_-lKX(X)≥ n-1, we study the lower bound of the anti-canonical volume and the upper bound of the anti-canonical stability index. The method can also be used to give similar bounds for polarised Calabi-Yau varieties.

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