4 problems

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Weak Campana–Peternell conjecture on bigness of nef tangent bundles
Weak Campana–Peternell conjecture. If the tangent bundle of a Fano manifold is nef, then it is also big.
Conjectureopenfano-manifolds nef-tangent-bundles positivityarXiv posted 2 days ago
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The Campana–Peternell–Demailly–Peternell–Schneider conjecture on Fano manifolds with nef tangent bundle
Let $X$ be a Fano manifold, meaning a smooth projective variety whose anticanonical divisor $-K_X$ is ample. Its tangent bundle $T_X$ is nef if the tautological line bundle on the…
Conjectureopenfano-varieties homogeneous-varieties nef-tangent-bundlesarXiv posted 2 days ago
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Greb–Wong–Höring–Peternell conjecture on canonical extensions and tangent-bundle positivity
Greb–Wong–Höring–Peternell conjecture. The tangent bundle $d4af_X$ is nef, respectively big and nef, if and only if some canonical extension $Z_X$ of $X$ is Stein, respectively aff…
Conjectureopencanonical-extensions complex-geometry nef-tangent-bundlesarXiv posted 2 days ago
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Dominating FT-manifold problem for Fano manifolds with nef tangent bundle
Dominating FT-manifold problem. There exists an FT-manifold $X$ with connected Dynkin diagram ${\mathcal D}(X)$ dominating $Y$ .
Problemopenfano-manifolds nef-tangent-bundles rational-curvesarXiv posted 2 days ago

Weak Campana–Peternell conjecture on bigness of nef tangent bundles