Compact K\"ahler manifolds with elliptic homotopy type
Jaume Amor\'os, Indranil Biswas
TL;DR
This paper characterizes simply connected compact K"ahler manifolds of low dimension with elliptic homotopy type using Hodge diamonds, and classifies specific examples like K"ahler surfaces and Fano threefolds.
Contribution
It provides a classification of low-dimensional simply connected K"ahler manifolds with elliptic homotopy type based on their Hodge structures.
Findings
Classification of simply connected K"ahler surfaces with elliptic homotopy type
Characterization of Fano threefolds with elliptic homotopy type
Use of Hodge diamonds to determine homotopy properties
Abstract
Simply connected compact K\"ahler 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 K\"ahler surfaces and Fano threefolds with elliptic homotopy type.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory