Sharp systolic inequalities for Kähler manifolds with positive scalar curvature attain equality on CP^n with Fubini-Study metric and imply Gromov's rational-essentialness conjecture.
A characterization of uniruled compact K \"ahler manifolds
6 Pith papers cite this work. Polarity classification is still indexing.
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Compact Kähler manifolds of algebraic dimension zero are essentially isogeneous to products of Kummer and simple manifolds; four-dimensional strictly simple ones are étale quotients of tori or holomorphically symplectic.
Pointwise isomorphic smooth families of projective non-uniruled manifolds over a Riemann surface are locally isomorphic over a dense open subset of the base.
Uniform weak RC-positivity of TX on a compact Kähler manifold X implies X is projective and rationally connected; the same condition on any holomorphic vector bundle E yields a Hermitian metric with positive mean curvature.
Weak spectral positivity implies rational connectedness and simple connectedness for compact Kähler manifolds and simple connectedness for even-dimensional Riemannian manifolds.
Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.
citing papers explorer
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Sharp systolic inequalities for K\"ahler manifolds
Sharp systolic inequalities for Kähler manifolds with positive scalar curvature attain equality on CP^n with Fubini-Study metric and imply Gromov's rational-essentialness conjecture.
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Bogomolov Decomposition and Compact K{\"a}hler Manifolds of Algebraic Dimension Zero
Compact Kähler manifolds of algebraic dimension zero are essentially isogeneous to products of Kummer and simple manifolds; four-dimensional strictly simple ones are étale quotients of tori or holomorphically symplectic.
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Local isomorphisms for families of projective non-unruled manifolds
Pointwise isomorphic smooth families of projective non-uniruled manifolds over a Riemann surface are locally isomorphic over a dense open subset of the base.
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Uniform weak RC-positivity and rational connectedness
Uniform weak RC-positivity of TX on a compact Kähler manifold X implies X is projective and rationally connected; the same condition on any holomorphic vector bundle E yields a Hermitian metric with positive mean curvature.
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Simply connectedness of K\"ahler and Riemannian manifolds via spectral estimates (with an appendix by Shiyu Zhang)
Weak spectral positivity implies rational connectedness and simple connectedness for compact Kähler manifolds and simple connectedness for even-dimensional Riemannian manifolds.
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Compact K\"ahler contact manifolds
Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.