Compact Kähler manifolds with elliptic homotopy type

2009/01/21 by Jaume Amorós, Indranil Biswas, Amorós, Jaume +1
Mathematics · #14P25 #55P62 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14P25 #msc:55P62

paper · pdf · doi:10.48550/arxiv.0901.3211

17 pages

arxiv created 2009/01/21 · openalex publication_date 2009/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.

Citations

• Infinitesimal computations in topology
• Quotients of products of curves, new surfaces with p_g=0 and their fundamental groups

Related

• Some results on compact Kahler manifolds with elliptic homotopy type
• Hodge decomposition theorem on compact d-Kähler manifolds
• On compact complex surfaces of Kähler rank one
• Elliptic Theory on Manifolds with Corners: II. Homotopy classification and K-Homology
• Higher-dimensional analogues of K3 surfaces