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arXiv · 2410.15457

A generalized non-vanishing theorem on surfaces

Jihao Liu·Lingyao Xie
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Abstract

We show that the anti-canonical bundle of any $\mathbb Q$-factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical non-vanishing theorem for surfaces polarized with pseudo-effective divisors. The latter answers a question of C. Fontanari.

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Jihao Liu, Lingyao Xie. 2024-10-20. A generalized non-vanishing theorem on surfaces. https://arxiv.org/abs/2410.15457

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