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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Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.
If a degenerating threefold has canonical singularities, the moduli space of pairs of P^3 and hypersurfaces is smooth at the corresponding point.
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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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Compact K\"ahler contact manifolds
Non-projective compact Kähler contact manifolds are projectivized tangent bundles of compact Kähler manifolds.
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Deformation of pairs of $\mathbb{P}^3$ and hypersurfaces
If a degenerating threefold has canonical singularities, the moduli space of pairs of P^3 and hypersurfaces is smooth at the corresponding point.