Log canonical pairs over varieties with maximal Albanese dimension

2018/01/02 by Zhengyu Hu, Hu, Zhengyu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1801.00739

openalex publication_date 2018/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,B) be a log canonical pair over a normal variety Z with maximal Albanese dimension. If K_X+B is relatively abundant over Z (for example, K_X+B is relatively big over Z), then we prove that K_X+B is abundant. In particular, the subadditvity of Kodaira dimensions κ(K_X+B) ≥ κ(K_F+B_F)+ κ(Z) holds, where F is a general fiber, K_F+B_F= (K_X+B)|_F, and κ(Z) means the Kodaira dimension of a smooth model of Z. We discuss several variants of this result in Section 4. We also give a remark on the log Iitaka conjecture for log canonical pairs in Section 5.

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• Note on Iitaka Conjecture C_n,m

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