Transcendental Hodge algebra

Misha Verbitsky ^[1]
1. [1] National Research University
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 2203-2218
Idioma: inglés
DOI: 10.1007/s00029-017-0307-9
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Resumen
- 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] .