Higher dimensional tautological inequalities and applications
Carlo Gasbarri (IRMA), Gianluca Pacienza (IRMA), Erwan Rousseau (IRMA)
TL;DR
This paper investigates the degeneracy of holomorphic mappings tangent to foliations on projective manifolds, employing higher-dimensional Ahlfors currents to establish significant degeneracy results.
Contribution
It introduces new degeneracy theorems for holomorphic mappings tangent to foliations using advanced techniques involving higher-dimensional Ahlfors currents.
Findings
Established strong degeneracy results for holomorphic mappings
Applied higher-dimensional Ahlfors currents in complex geometry
Provided new insights into foliations on projective manifolds
Abstract
We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Quantum chaos and dynamical systems