This research reveals the existence of ruled divisors in projective holomorphic symplectic manifolds, suggesting new pathways for understanding their geometry.
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 Q̄ 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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Beri et al. (2025) studied this question.
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