2021/05/29 by Shin‐ichi Matsumura, Matsumura, Shin-ichi, Juanyong Wang +1 · 3 citations
Mathematics · #14E30 (Primary) 32Q30 #32J25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2105.14308
openalex publication_date 2021/05/29 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28
In this paper, we establish a structure theorem for projective klt pairs (X,Δ) with nef anti-log canonical divisor; specifically, we prove that, up to replacing X with a finite quasi-étale cover, X admits a locally trivial rationally connected fibration onto a projective klt variety with numerically trivial canonical divisor. This structure theorem generalizes previous works for smooth projective varieties and reduces several structure problems to the singular Beauville-Bogomolov decomposition for Calabi-Yau varieties. As an application, projective varieties of klt Calabi-Yau type, which naturally appear as an outcome of the Log Minimal Model Program, are decomposed into building block varieties: rationally connected varieties and Calabi-Yau varieties.