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arXiv · 2111.04270

On the existence of rational curves on projective hyperk\"ahler fourfolds

Haidong Liu
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Abstract

We show that if $X$ is a projective hyperk\"ahler fourfold and there exists a nonzero effective divisor $D$ which is not of bi-elliptic type and contained in the boundary of the nef cone of $X$, then $X$ contains a rational curve. This is a very special case of Oguiso's conjecture for projective hyperk\"ahler fourfolds.

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Haidong Liu. 2021-11-08. On the existence of rational curves on projective hyperk\"ahler fourfolds. https://arxiv.org/abs/2111.04270

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