New numerical invariants called hyperbolic indices, defined via liftable directed currents on Demailly-Semple towers, give a sufficient condition for Kobayashi hyperbolicity and grow at least linearly in degree for general hypersurfaces.
Regularity of the volume function.arXiv:2505.14495,
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Quantitative hyperbolicity for complex manifolds via numerical invariants
New numerical invariants called hyperbolic indices, defined via liftable directed currents on Demailly-Semple towers, give a sufficient condition for Kobayashi hyperbolicity and grow at least linearly in degree for general hypersurfaces.