par Verbitskiy, Misha
Référence Selecta mathematica, New series, 23, 3, page (2203-2218)
Publication Publié, 2017-07
Article révisé par les pairs
Résumé : The transcendental Hodge lattice of a projective manifold M is the smallest Hodge substructure in pth cohomology which contains all holomorphic p-forms. We prove that the direct sum of all transcendental Hodge lattices has a natural algebraic structure, and compute this algebra explicitly for a hyperkähler manifold. As an application, we obtain a theorem about dimension of a compact torus T admitting a holomorphic symplectic embedding to a hyperkähler manifold M. If M is generic in a d-dimensional family of deformations, then dim T≥ 2 [ ( d + 1 ) / 2 ].