| Résume | In the first part of this talk, I give a complete description of the divisorial
part of the base locus of big and nef line bundles on irreducible symplectic
varieties (under certain conditions). This is a generalization of well-known
results of Mayer and Saint-Donat for K3 surfaces. In the second part, I will
present what is currently known on the non-divisorial part, including the
results of an ongoing cooperation with Daniele Agostini.
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