arXiv subjects
Publications and source records attributed to Peichu Hu.
We investigate the value distribution of holomorphic maps defined on one class of Kähler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main Theorem for complex Euclidean spaces and complex unit balls.
By using techniques of holomorphic jets and Jacobian fields, we devise a non-equidistribution theory of holomorphic curves into complex projective varieties intersecting normal crossing divisors. Based on this theory established, we prove the Griffiths conjecture and the Green-Griffiths conjecture in Nevanlinna theory and algebraic geometry.
We consider the algebraic degeneracy of holomorphic curves from a point of view of meromorphic vector fields. Employing the notion of Jocabian sections introduced by W. Stoll, we establish a Second Main Theorem type inequality. As consequences, several algebraic degeneracy theorems are obtained for holomorphic curves into a complex projective variety.