A universal affine bundle over compact complex manifolds with invariant measures provides canonical potentials for dd^c-closed (1,1)-forms and reduces torsor-lifting obstructions to compact subtori.
A characterization of uniruled compact K\"ahler manifolds
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We adapt Bost's algebraicity characterization to the situation of a germ in a compact K\"ahler manifold. As a consequence, we extend the algebraic integrability criteria of Campana-P\u{a}un and of Druel to foliations on compact K\"ahler manifolds. As an application, we prove that a compact K\"ahler manifold is uniruled if and only if its canonical line bundle is not pseudoeffective.
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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.
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.
Compact Kähler manifolds of algebraic dimension zero are isogenous to products of Kummer and simple manifolds; four-dimensional strictly simple ones are étale tori quotients or holomorphically symplectic.
Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.
citing papers explorer
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Universal affine bundles for compact complex manifolds
A universal affine bundle over compact complex manifolds with invariant measures provides canonical potentials for dd^c-closed (1,1)-forms and reduces torsor-lifting obstructions to compact subtori.
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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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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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Bogomolov decomposition and compact K{\"a}hler manifolds of algebraic dimension zero
Compact Kähler manifolds of algebraic dimension zero are isogenous to products of Kummer and simple manifolds; four-dimensional strictly simple ones are étale tori quotients or holomorphically symplectic.
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Compact K\"ahler contact manifolds
Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.