2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225663Let $X\to¶^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $¶^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space $\mathrm{Def}(X)$ of deformations of $X$. We extend his result by proving that if the Lagrangian fibration admits a section, then there is a codimension two family of deformations which also preserve the section.9 pagesAlgebraic Geometry53C26; 14D06; 14J60text