Minimal projective varieties satisfying Miyaoka's equality

2024/04/11 by Masataka Iwai, Shinichi Matsumura, Iwai, Masataka +3
Mathematics · #32Q26 #32Q30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Primary 14E30 #Secondary 14D06

paper · pdf · doi:10.48550/arxiv.2404.07568

openalex publication_date 2024/04/11 · openalex created_date 2024/04/13 · openalex updated_date 2026/07/30

Abstract

In this paper, we establish a structure theorem for minimal projective klt varieties X that satisfiy Miyaoka's equality 3c₂(X) = c₁(X)². Specifically, we prove that the canonical divisor K_X is semi-ample and that the Kodaira dimension κ(K_X) is either 0, 1, or 2. Furthermore, based on this abundance result, we show that a maximally quasi-étale cover of X is smooth, and we describe explicitly the structure of the Iitaka fibration. Additionally, we prove a similar result for projective klt varieties with a nef anti-canonical divisor.

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• Iitaka's C_n,m conjecture for 3-folds in positive characteristic
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