Degrees $d⩾(\sqrt{n}\log n{)}^n$ and $d⩾(n\log n{)}^n$ in the Conjectures of Green-Griffiths and of Kobayashi

Joel Merker, The-Anh Ta

Once first answers in any dimension to the Green-Griffiths and Kobayashi conjectures for generic algebraic hypersurfaces ${\mathbb{X}}^{n-1}\subset {\mathbb{P}}^n(\mathbb{C})$ have be…