Strictly nef divisors on singular threefolds

2021/05/17 by Guolei Zhong, Zhong, Guolei
Mathematics · #Algebraic Geometry and Number Theory #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2105.07681

Abstract

Let X be a normal projective threefold with mild singularities, and L_X a strictly nef ℚ-divisor on X. First, we show the ampleness of K_X+tL_X with sufficiently large t if either the Kodaira dimension κ(X)≠ 0 or the augmented irregularity q^∘(X)≠ 0. Second, we show that, if (X,Δ) is a projective klt threefold pair with the anti-log canonical divisor -(K_X+Δ) being strictly nef, then X is rationally connected.

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