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arXiv · 2511.22329

Maximal variation of linear systems

Arnaud Beauville
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Abstract

Let X be a smooth projective complex variety, and L a line bundle on X . We say that the linear system |L| has maximal variation if its elements have the maximum number dim|L| of moduli. We discuss some cases where this situation is expected: hypersurfaces, double coverings of the projective space, K3 surfaces, hyperk\"ahler manifolds, and abelian varieties.

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Arnaud Beauville. 2025-11-27. Maximal variation of linear systems. https://arxiv.org/abs/2511.22329

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