On the Zariski density of rational curves on IHS manifolds

Pietro Beri; Giovanni Mongardi; Gianluca Pacienza

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arXiv · 2502.09349

On the Zariski density of rational curves on IHS manifolds

Pietro Beri·Giovanni Mongardi·Gianluca Pacienza

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Abstract

In analogy with recent works on $K3$ surfaces, we study the existence of infinitely many ruled divisors on projective irreducible holomorphic symplectic (IHS) manifolds. We prove such an existence result for any projective IHS manifold of $K3^{[n]}$ or generalized Kummer type which is not a variety defined over $\overline{\mathbb{Q}}$ with Picard number one or maximal. The result is obtained as a combination of the regeneration principle and of a generalization to higher dimension of a controlled degeneration technique, invented by Chen, Gounelas and Liedtke in dimension 2.

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Pietro Beri, Giovanni Mongardi, Gianluca Pacienza. 2025-02-13. On the Zariski density of rational curves on IHS manifolds. https://arxiv.org/abs/2502.09349

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