In this paper we prove a conjecture of Markman about the shape of the monodromy group of irreducible holomorphic symplectic manifolds of OG10 type. As a corollary, we also compute the locally trivial monodromy group of the underlying singular symplectic variety.

In this paper we consider irreducible holomorphic symplectic sixfolds of the sporadic deformation type discovered by O'Grady, and their symplectic birational transformations of finite order. We study the induced isometries on the Beauville-Bogomolov-Fujiki lattice, classifying all possible invariant and coinvariant sublattices, and providing explicit examples. As a consequence, we show that the isometry induced by a symplectic automorphism of finite order is necessarily trivial. This paper is a first step towards the classification of all finite groups of symplectic birational transformations.

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In this paper, we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterization of Kähler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian fibrations of smooth cubic fourfolds.