2003/12/01 by Claire Voisin · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics #Complex dimension #Complex projective space #Dimension (graph theory) #Geometry and complex manifolds #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Homotopy sphere #Kodaira dimension #Kähler manifold #Manifold (fluid mechanics) #Mathematics #Projective space #Projective test #Pure mathematics #Regular homotopy #Simply connected space #Topology (electrical circuits) #Type (biology) #math.AG #math.SG #n-connected
paper · pdf · doi:10.1007/s00222-003-0352-1
published as Inventiones Math. Volume 157, Number 2, (2004), 329 - 343 · To appear in Inventiones Math
arxiv created 2003/12/01 · openalex publication_date 2004/07/09 · arxiv updated 2015/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective manifold, which solves negatively Kodaira's problem. We give both non simply connected (of dimension at least 4) and simply connected (of dimension at least 6) such examples.