4 papers
On Ahlfors currents
Dinh Tuan Huynh, Song-Yan Xie
We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve $f: \m…
Big Picard Theorem for jet differentials and Non-archimedean Ax-Lindemann Theorem
Dinh Tuan Huynh, Ruiran Sun, Song-Yan Xie
By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As app…
On the Weyl-Ahlfors theory of derived curves
Dinh Tuan Huynh, Song-Yan Xie
For derived curves intersecting a family of decomposable hyperplanes in subgeneral position, we obtain an analog of Cartan-Nochka Second Main Theorem, generalizing a classical resu…
On the set of divisors with zero geometric defect
Dinh Tuan Huynh, Duc-Viet Vu
Let be a transcendental holomorphic curve into a complex projective manifold . Let be a very ample line bundle on . Let be a very generic holomo…