A remark on generalized abundance for surfaces

2023/07/28 by Fontanari, Claudio
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.15686

Abstract

Let (X, Δ) be a projective klt pair of dimension 2 and let L be a nef ℚ-divisor on X such that K_X + Δ+ L is nef. As a complement to the Generalized Abundance Conjecture by Lazić and Peternell, we prove that if K_X + Δ and L are not proportional modulo numerical equivalence, then K_X + Δ+ L is semiample. An example due to Lazić shows that this is no longer true in any dimension n ≥ 3.

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