Maximal variation of linear systems
Algebraic Geometry
2026-01-21 v4
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, hyperkahler manifolds, and abelian varieties.
Cite
@article{arxiv.2511.22329,
title = {Maximal variation of linear systems},
author = {Arnaud Beauville},
journal= {arXiv preprint arXiv:2511.22329},
year = {2026}
}
Comments
Added results of B. Bakker for the K3 case