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arXiv · 2312.09441

A question about generalized nonvanishing

Claudio Fontanari
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Abstract

Let $(X,\Delta)$ be a projective, $\mathbb{Q}$-factorial log canonical pair and let $L$ be a pseudoeffective $\mathbb{Q}$-divisor on $X$ such that $K_X + \Delta + L$ is pseudoeffective. Is there an effective $\mathbb{Q}$-divisor $M$ on $X$ such that $K_X + \Delta + L$ is numerically equivalent to $M$? We are not aware of any counterexamples, but the answer is not completely clear even in the case of surfaces.

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Claudio Fontanari. 2023-10-17. A question about generalized nonvanishing. https://arxiv.org/abs/2312.09441

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