Some non-vanishing results on log canonical pairs of dimension 4

2019/06/27 by Fanjun Meng, Meng, Fanjun
Mathematics · #14E30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1906.11451

openalex publication_date 2019/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,Δ) be a log canonical pair over ℂ with X a normal projective variety, Δ an effective ℚ-divisor, and K_X+Δ nef. We give a non-vanishing criterion for K_X+Δ in dimension n with X uniruled, assuming various conjectures of LMMP in dimensions (up to) n-1 or n, and a semi-ampleness criterion in the irregular case. In particular, we obtain that if X is a uniruled 4-fold, then κ(K_X+Δ)≥ 0 and if X is a 4-fold with q(X)>0, then K_X+Δ is semi-ample.

Citations

• Termination of pseudo-effective 4-fold flips

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