Abstract
For the last fifteen years, numerous authors have studied the birational geometry of projective irreducible holomorphic symplectic varieties X, seeking to relate extremal contractions $$ X \to X ^\prime $$ to properties of the Hodge structures on $$ H^2 \left( {X,{\Bbb Z}} \right)\,and \,H_2 \left({X,{\Bbb Z}} \right) $$ , regarded as lattices under the Beauville-Bogomolov form. Significant contributions have been made by Huybrechts, Markman, O’Grady, Verbitsky, and many others [Huy99], [Mar08], [O’G99], [Ver13], see also [Huy11].
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