We prove that the bimeromorphic class of a hyperkähler manifold deformation equivalent to O'Grady's six dimensional one is determined by the Hodge structure of its Beauville-Bogomolov lattice by showing that the monodromy group is maximal. As applications, we give the structure for the Kähler and the birational Kähler cones in this deformation class and we prove that the existence of a square zero divisor implies the existence a rational lagrangian fibration with fixed fibre types.

中文翻译：

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奥格雷迪的六重一律和两分几何

通过证明单峰基团最大，我们证明了等于O'Grady六维一维的超kähler流形变形的双态类由其Beauville-Bogomolov晶格的Hodge结构确定。作为应用，我们给出了此变形类中的Kähler锥和双边Kähler锥的结构，并证明了平方零除数的存在意味着存在固定纤维类型的有理拉格朗日纤维。