2017/03/31 by Nikon Kurnosov, Andrey Soldatenkov, Misha Verbitsky · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Cohomology #Embedding #Geometry #Geometry and complex manifolds #Hodge structure #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Space (punctuation) #Torus #math.AG #math.DG
paper · pdf · doi:10.1016/j.aim.2019.04.060
published as Advances in Mathematics Volume 351, 31 July 2019, Pages 275-295 · 25 pages; to appear in Adv. Math
arxiv created 2019/04/25 · openalex publication_date 2019/05/17 · crossref created 2019/05/17 · crossref issued 2019/07/01 · crossref published 2019/07/01 · crossref published-print 2019/07/01 · arxiv updated 2021/09/20 · crossref deposited 2025/09/11 · openalex created_date 2025/10/10 · crossref indexed 2026/02/08 · openalex updated_date 2026/08/05
Let M be a simple hyperkahler manifold. Kuga-Satake construction gives an embedding of H2(M,C) into the second cohomology of a torus, compatible with the Hodge structure. We construct a torus T and an embedding of the graded cohomology space H^*(M,C) → H*+l(T,C) for some l, which is compatible with the Hodge structures and the Poincare pairing. Moreover, this embedding is compatible with an action of the Lie algebra generated by all Lefschetz sl(2)-triples on M.